Publications - Siegfried M. Rump

• D. Chaykin, C. Jansson, F. Keil, M. Lange, K.T. Ohlhus, and S.M. Rump. Rigorous Lower Bounds for the Ground State Energy of Molecules by Employing Necessary N-Representability Conditions. Journal of Chemical Theory and Computation, 2020. url = https://doi.org/10.1021/acs.jctc.0c00497. (doi:10.1021/acs.jctc.0c00497)
• R. Kobayashi, M. Lange, A. Minamihata, and S.M. Rump. Verified Inclusion of a Basis of the Null space. Reliable Computing, 27:26–41, 2020. (PDF)
• M. Lange and S.M. Rump. Verified inclusions of a nearest matrix of specified rank deficiency via a generalization of Wedin's sin (θ) theorem. BIT Numerical Mathematics, to appear, 2020. (PDF)
• S.M. Rump. Addendum to "On recurrences converging to the wrong limit in finite precision and some new examples". Electronic Transactions on Numerical Analysis (ETNA), 52:571–575, 2020. https://doi.org/10.1553/etna_vol52s575. (PDF)
• S.M. Rump. On recurrences converging to the wrong limit in finite precision and some new examples. Electronic Transactions on Numerical Analysis (ETNA), 52:358–369, 2020. https://doi.org/10.1553/etna_vol52s358. (PDF)
• S.M. Rump. Verified bounds for the determinant of real or complex point or interval matrices. Journal of Computational and Applied Mathematics (JCAM), 372, 2020. 11 pages, Article 112610, https://doi.org/10.1016/j.cam.2019.112610. (PDF)
• F. Bünger and S.M. Rump. Complex Disk Products and Cartesian Ovals. Journal of Geometry, 110(45), 2019. 8pages, https://doi.org/10.1007/s00022-019-0502-2. (PDF)
• F. Bünger and S.M. Rump. Lower bounds for the smallest singular value of certain Toeplitz-like triangular matrices with linearly increasing diagonal entries. Integral Equations and Operator Theory, 91:39, 2019. (PDF)
• F. Bünger and S.M. Rump. The determinant of a complex matrix and Gershgorin circles. Electronic Journal of Linear Algebra (ELA), 35:181–186, 2019. (PDF)
• M. Lange and S.M. Rump. Sharp estimates for perturbation errors in summations. Math. of Comp., 88:349–368, 2019. (PDF)
• S.M. Rump. Bounds for the Determinant by Gershgorin Circles. Linear Algebra and its Application (LAA), 563:215–219, 2019. (PDF) (doi:10.1016/j.laa.2018.10.020)
• S.M. Rump. Error bounds for computer arithmetics. Summary of the plenary talk at ARITH26, Kyoto, IEEE Xplore, 2019. (PDF)
• S.M. Rump and P. Batra. Addendum to the determinant of a perturbed identity matrix. Linear Algebra and its Applications (LAA), 565:309–312, 2019. (PDF)
• C.-P. Jeannerod and S.M. Rump. On relative errors of floating-point operations: Optimal bounds and applications. Mathematics of Computation, 87:803–819, 2018. (PDF) (doi:10.1090/mcom/3234)
• S. Oishi, K. Ichihara, M. Kashiwagi, K. Kimura, X. Liu, H. Masai, Y. Morikura, T. Ogita, K. Ozaki, S.M. Rump, K. Sekine, A. Takayasu, and N. Yamanaka. Principle of Verified Numerical Computations. Corona publisher, 2018. 311 pages, Tokyo, Japan, in Japanese. (PDF)
• S.M. Rump. Estimates of the determinant of a perturbed identity matrix. Linear Algebra and its Applications (LAA), 558:101–107, 2018. (PDF) (doi:10.1016/j.laa.2018.08.009)
• S.M. Rump. Linear Systems in Matlab with Zero Residual. Reliable Computing, 26:56–66, 2018. (PDF)
• S.M. Rump. Mathematically Rigorous Global Optimization in Floating-Point Arithmetic. Optimization Methods & Software, 33(4–6):771–798, 2018. (PDF) (doi:10.1080/10556788.2018.1435649)
• F. Bünger and S.M. Rump. Yet more elementary proofs that the determinant of a symplectic matrix is 1. Linear Algebra and its Applications (LAA), 515:87–95, 2017. (PDF) (doi:10.1016/j.laa.2016.11.014)
• M. Lange and S.M. Rump. Error estimates for the summation of real numbers with application to floating-point summation. BIT, 57:927–941, 2017. (PDF) (doi:10.1007/s10543-017-0658-9)
• M. Lange and S.M. Rump. Faithfully Rounded Floating-point Computations. submitted for publication, 2017. (PDF)
• L. Lehmann, M. Radons, S.M. Rump, and C. Strohm. Sign controlled solvers for the absolute value equation with an application to support vector machines. submitted for publication, 2017. (PDF)
• S.M. Rump. IEEE754 precision-k base-β arithmetic inherited by precision-mbase-β; arithmeticfor k < m . ACM Trans. Math. Software, 43(3), 2017. (PDF) (doi:10.1145/2785965)
• F. Bünger and S.M. Rump. A short note on the convexity of interval matrix-vector products. Reliable Computing, 21:74–79, 2016. (PDF)
• I.S. Kotsireas, S.M. Rump, and C.K. Yap, editors. Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Berlin, Germany, November 11-13, 2015, Revised Selected Papers, volume 9582 of Lecture Notes in Computer Science. Springer, 2016. (doi:10.1007/978-3-319-32859-1)
• K. Ozaki, F. Bünger, T. Ogita, S. Oishi, and S.M. Rump. Simple floating-point filters for the two-dimensional orientation problem. BIT Numerical Mathematics, 56(2):729–749, 2016. (PDF) (doi:10.1007/s10543-015-0574-9)
• S.M. Rump. Gleitkommaarithmetik auf dem Prüfstand [Wie werden verifiziert(e) numerische Lösungen berechnet?]. Jahresbericht der Deutschen Mathematiker-Vereinigung, 118(3):179–226, 2016. (PDF) (doi:10.1365/s13291-016-0138-1)
• S. Rump, T. Ogita, Y. Morikura, and S. Oishi. Interval arithmetic with fixed rounding mode. Nonlinear Theory and its Aplications (IEICE), 7(3):362–373, 2016. (PDF) (doi:10.1587/nolta.7.362)
• S.M. Rump. Computable backward error bounds for basic algorithms in linear algebra. Nonlinear Theory and Its Applications, IEICE, 6:1–4, 2015. (PDF)
• S.M. Rump. Interval Arithmetics. In B. Engquist, editor, Encyclopedia of Applied and Computational Mathematics, pages 712–716. Springer Berlin Heidelberg, 2015. (doi:10.1007/978-3-540-70529-1)
• S.M. Rump. The componentwise structured and unstructured backward error can be arbitrarily far apart. SIAM J. Matrix Anal. Appl. (SIMAX), 36(2):385–392, 2015. (PDF)
• S.M. Rump and M. Lange. On the Definition of Unit Roundoff. BIT Numerical Mathematics, 56(1):309–317, 2015. (PDF) (doi:10.1007/s10543-015-0554-0)
• S.M. Rump and Kashiwagi M. Implementation and improvements of affine arithmetic. Nonlinear Theory and Its Applications, IEICE,, 2(3):1101–1119, 2015. (PDF)
• S.M. Rump, F. Bünger, and C.-P. Jeannerod. Improved Error Bounds for Floating-Point Products and Horner's Scheme. BIT Numerical Mathematics, 56(1):293–307, 2015. (PDF) (doi:10.1007/s10543-015-0555-z)
• S.M. Rump. Verified bounds for the p-norm condition number. Reliable Computing, Vol. 20, pp. 45-52, 2014. (PDF)
• S.M. Rump. Verified sharp bounds for the real gamma function over the entire floating-point range. Nonlinear Theory and Its Applications (NOLTA), IEICE, Vol.E5-N,No.3, July, 2014. (PDF)
• S.M. Rump and C.-P. Jeannerod. Improved backward error bounds for LU and Cholesky factorizations. SIAM. J. Matrix Anal. & Appl. (SIMAX), 35(2):684–698, 2014. (PDF) (doi:10.1137/130927231)
• C.-P. Jeannerod and S.M. Rump. Improved error bounds for inner products in floating-point arithmetic. SIAM. J. Matrix Anal. & Appl. (SIMAX), 34(2):338–344, 2013. (PDF)
• T. Nishi, S.M. Rump, and S. Oishi. A consideration on the condition number of extremely ill-conditioned matrices. Circuit Theory and Design (ECCTD), 2013 European Conference on, pages 1–4, 2013. (doi:10.1109/ECCTD.2013.6662260)
• K. Ozaki, T. Ogita, S. Oishi, and S.M. Rump. Generalization of error-free transformation for matrix multiplication and its application. Nonlinear Theory and Its Applications, IEICE, 4(1):2–11, 2013.
• S.M. Rump. Accurate solution of dense linear systems, Part I: Algorithms in rounding to nearest. Journal of Computational and Applied Mathematics (JCAM), 242:157–184, 2013. (PDF)
• S.M. Rump. Accurate solution of dense linear systems, Part II: Algorithms using directed rounding. Journal of Computational and Applied Mathematics (JCAM), 242:185–212, 2013. (PDF)
• S.M. Rump. Improved componentwise verified error bounds for least squares problems and underdetermined linear systems. Numerical Algorithms, 66:309–322, 2013. (PDF)
• S.M. Rump, T. Ogita, and S. Oishi. Interval Arithmetic without Changing the Rounding Mode. submitted for publication, 2013.
• K. Ozaki, T. Ogita, S. Oishi, and S.M. Rump. Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications. Numerical Algorithms, 59(1), 2012. (PDF)
• K. Ozaki, T. Ogita, S.M. Rump, and S. Oishi. Fast algorithms for floating-point interval matrix multiplication. Journal of Computational and Applied Mathematics, 236(7):1795–1814, 2012. http://www.sciencedirect.com/science/article/pii/S0377042711005449. (doi:10.1016/j.cam.2011.10.011)
• S.M. Rump. Error estimation of floating-point summation and dot product. BIT Numerical Mathematics, 52(1):201–220, 2012. (PDF)
• S.M. Rump. Fast Interval Matrix Multiplication. Numerical Algorithms, 61(1):1–34, 2012. (PDF)
• S.M. Rump. Interval Arithmetic Over Finitely Many Endpoints. BIT Numerical Mathematics, 52(4):1059–1075, 2012. (PDF)
• S.M. Rump. Verified Bounds for Least Squares Problems and Underdetermined Linear Systems. SIAM J. Matrix Anal. Appl. (SIMAX), 33(1):130–148, 2012. (PDF)
• T. Nishi, S.M. Rump, and S. Oishi. On the generation of very ill-conditioned integer matrices. Nonlinear Theory and Its Applications, IEICE, 2(2):226–245, 2011. (PDF)
• S.M. Rump. Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse. BIT Numerical Mathematics, 51(2):367–384, 2011. (PDF)
• B. Kearfott, M. Nakao, S. Neumaier, A. Rump, S.P. Shary, and P. Van Hentenryck. Standardized notation in interval analysis. Reliable Computing, 15(1):7–13, 2010. (PDF)
• S. Miyajima, T. Ogita, S.M. Rump, and S. Oishi. Fast Verification of All Eigenpairs in Symmetric Positive Definite Generalized Eigenvalue Problem. Reliable Computing, 14:24–45, 2010. (PDF)
• T. Nishi, S.M. Rump, and S. Oishi. Some properties and generation methods of integer matrices with large condition number. IEICE technical Report, Circuits and Systems, 110(86):13–18, 2010. http://ci.nii.ac.jp/naid/110007890169.
• S.M. Rump. A Model Problem for Global Optimization. In Nonlinear Theory and Its Applications (NOLTA), volume 1, pages 1–6. IEICE, 2010. (PDF)
• S.M. Rump. Accurate and Reliable Computing in Floating-Point Arithmetic. In K. Fukuda et al., editor, Proceedings of the Third International Congress on Mathematical Software, Kobe, Japan, September 13-17, 2010 (ICMS 2010), volume 6327 of Lecture Notes in Computer Science (LNCS), pages 105–108, 2010. http://www.springerlink.com/content/b201872815051165/.
• S.M. Rump. Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19:287–449, 2010. (PDF)
• S.M. Rump and S. Graillat. Verified error bounds for multiple roots of systems of nonlinear equations. Numerical Algorithms, 54(3):359–377, 2010. (PDF) (doi:10.1007/s11075-009-9339-3)
• S.M. Rump, T. Ogita, and S. Oishi. Fast high precision summation. Nonlinear Theory and Its Applications (NOLTA), IEICE, 1(1):2–24, 2010. [received the "NOLTA Best Paper Award" by the IEICE Engineering Sciences Society]. (PDF)
• A. Berman, Ch. Krattenthaler, S.M. Rump, I. Spitkovsky, and F. Zhang. Short biography of Shmuel Friedland for his special LAA volume. Linear Algebra and its Applications (LAA), 431(12):2277–2284, 2009. (PDF)
• S. Oishi, T. Ogita, and S. M. Rump. Iterative Refinement for Ill-conditioned Linear Equations. Japan J. Indust. Appl. Math., 26(2):465–476, 2009.
• K. Ozaki, T. Ogita, S.M. Rump, and S. Oishi. Adaptive and Efficient Algorithm for 2D Orientation Problem. Japan J. Indust. Appl. Math., 26:215–231, 2009. (PDF)
• S.M. Rump. Error-Free Transformations and ill-conditioned problems. In Proceedings of the ``International workshop on verified computations and related topics'', University of Karlsruhe, March 7-10, 2009. (PDF)
• S.M. Rump. Inversion of extremely ill-conditioned matrices in floating-point. Japan J. Indust. Appl. Math. (JJIAM), 26:249–277, 2009. (PDF)
• S.M. Rump. Ultimately Fast Accurate Summation. SIAM Journal on Scientific Computing (SISC), 31(5):3466–3502, 2009. (PDF)
• S. M. Rump and S. Oishi. Verified Error Bounds for Double Roots of Nonlinear Equations. In 2009 International Symposium on Nonlinear Theory and its Applications, NOLTA'09, Sapporo, Japan, 2009. (PDF)
• S.M. Rump and S. Oishi. Verified computation of a disc containing exactly k roots of a univariate nonlinear function. Nonlinear Theory and Its Applications (NOLTA), IEICE, 1(1):1–8, 2009. (PDF)
• S.M. Rump and H. Sekigawa. The ratio between the Toeplitz and the unstructured condition number. Operator Theory: Advances and Applications, 199:397–419, 2009. (PDF)
• S.M. Rump, P. Zimmermann, S. Boldo, and G. Melquiond. Computing predecessor and successor in rounding to nearest. BIT Numerical Mathematics, 49(2):419–431, 2009. (PDF)
• S.M. Rump, P. Zimmermann, S. Boldo, and G. Melquiond. Interval operations in rounding to nearest. accepted for publication in BIT, 2009. (PDF)
• S. Graillat, J.-L. Lamotte, S.M. Rump, and S. Markov. Interval arithmetic on the Cell processor. In IMACS— 13th International Symposium on Scientific Computing Computer Arithmetic and Verified Numerical Computations, El Paso, Texas, USA, Sep. 29 – Oct. 3, 2008, pages 54–54, 2008. (PDF)
• T. Nishi, T. Ogita, S. Oishi, and S. M. Rump. A Method for the Generation of a Class of Ill-conditioned Matrices. In 2008 International Symposium on Nonlinear Theory and its Applications, NOLTA'08, Budapest, Hungary, September 7-10, pages 53–56, 2008. (PDF)
• T. Ogita, S.M. Rump, and S. Oishi. Verification of positive definiteness for large sparse matrices, 2008.
• S. Oishi, T. Ogita, and S. M. Rump. Iterative Refinement for Ill-conditioned Linear Equations. In 2008 International Symposium on Nonlinear Theory and its Applications, NOLTA'08, Budapest, Hungary, September 7-10, pages 516–519, 2008. (PDF)
• K. Ozaki, T. Ogita, S. M. Rump, and S. Oishi. Accurate matrix multiplication by using level 3 BLAS operation. In Proceedings of the 2008 International Symposium on Nonlinear Theory and its Applications, NOLTA'08, Budapest, Hungary, pages 508–511. IEICE, 2008. (PDF)
• S.M. Rump, T. Ogita, and S. Oishi. Accurate floating-point summation part I: Faithful rounding. SIAM J. Sci. Comput., 31(1):189–224, 2008. (PDF)
• S.M. Rump, T. Ogita, and S. Oishi. Accurate floating-point summation part II: Sign, K-fold faithful and rounding to nearest. Siam J. Sci. Comput., 31(2):1269–1302, 2008. (PDF)
• N. Yamanaka, T. Ogita, S.M. Rump, and S. Oishi. A Parallel Algorithm for Accurate Dot Product. Parallel Computing, 34(6–8):392–410, 2008. (PDF)
• S. Oishi, K. Tanabe, T. Ogita, and S.M. Rump. Convergence of Rump's method for inverting arbitrarily ill-conditioned matrices. J. Comput. Appl. Math., 205(1):533–544, 2007. (PDF) (doi:10.1016/j.cam.2006.05.022)
• K. Ozaki, T. Ogita, S. M. Rump, and S. Oishi. Accurate matrix multiplication with multiple floating-point numbers. In Proceedings of 2007 International Symposium on Nonlinear Theory and its Applications, Vancouver, Canada, September 16-19, 2007. (PDF)
• S.M. Rump and P. Zimmermann. Interval operations in rounding to nearest. submitted for publication, 2007. (PDF)
• G. Alefeld, M.T. Nakao, and S.M. Rump. Preface. Journal of Computational and Applied Mathematics (JCAM), 199(2):197–198, 2006. Special issue on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2004).
• V. Kreinovich and S.M. Rump. Towards Optimal Use of Multi-Precision Arithmetic: A Remark. Reliable Computing, 12:365–369, 2006. (PDF)
• K. Ozaki, T. Ogita, S. Miyajima, S. Oishi, and S.M. Rump. A method of obtaining verified solutions for linear systems suited for Java. Journal of Computational and Applied Mathematics (JCAM), 199(2):337–344, 2006. Special issue on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2004). (PDF)
• K. Ozaki, T. Ogita, S.M. Rump, and S. Oishi. Fast and robust algorithm for geometric predicates using floating-point arithmetic. Trans. Japan Soc. Ind. Appl. Math. (JSIAM), 4(16):553–562, 2006. (in Japanese). (PDF)
• S.M. Rump. Eigenvalues, pseudospectrum and structured perturbations. Linear Algebra and its Applications (LAA), 413:567–593, 2006. (PDF)
• S.M. Rump. Error bounds for extremely ill-conditioned problems. In Proceedings of 2006 International Symposium on Nonlinear Theory and its Applications, Bologna, Italy, September 11-14, 2006. (PDF)
• S.M. Rump. INTLAB - Interval Laboratory, the Matlab toolbox for verified computations, Version 5.3, 2006. http://www.ti3.tu-harburg.de/intlab/.
• S.M. Rump. Verification of Positive Definiteness. BIT Numerical Mathematics, 46:433–452, 2006. (PDF)
• S.M. Rump and T. Ogita. Super-fast validated solution of linear systems. Journal of Computational and Applied Mathematics (JCAM), 199(2):199–206, 2006. Special issue on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2004). (PDF)
• S. Friedland, D. Hershkowitz, and S.M. Rump. Positive entries of stable matrices. Electronic Journal of Linear Algebra (ELA), 12:17–24, 2005. (PDF)
• A. Hailer and S.M. Rump. Evaluation of Hedge Effectiveness Tests. Journal of Derivatives Accounting (JDA), 2(1):31–52, 2005. (PDF)
• A.C. Hailer and S.M. Rump. Evaluierung von Hedge-Effektivitätstests. Zeitschrift für das gesamte Kreditwesen, 58(20):1089–1097, 2005.
• T. Ogita, S.M. Rump, and S. Oishi. Verified Solutions of Sparse Linear Systems by LU factorization, 2005. (PDF)
• T. Ogita, S.M. Rump, and S. Oishi. Accurate sum and dot product. SIAM Journal on Scientific Computing (SISC), 26(6):1955–1988, 2005. (PDF)
• T. Ogita, S.M. Rump, and S. Oishi. Verified solution of linear systems without directed rounding. Technical Report 2005-04, Advanced Research Institute for Science and Engineering, Waseda University, Tokyo, Japan, 2005. (PDF)
• T. Ohta, T. Ogita, S.M. Rump, and S. Oishi. A Method of Verified Numerical Computation for Ill-conditioned Linear System of Equations. Journal of JSIAM, 15(3):269–287, 2005.
• T. Ohta, T. Ogita, S.M. Rump, and S. Oishi. Numerical Method for Dense Linear Systems with Arbitrariliy Ill-conditioned Matrices. In Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications, Bruge, Belgium, October 18–21, pages 745–748, 2005. (PDF)
• T. Ohta, T. Ogita, S.M. Rump, and S. Oishi. Numerical Verification Method for Arbitrarily Ill-conditioned Linear Systems. Transactions on the Japan Society for Industrial and Applied Mathematics (Trans. JSIAM), 15(3):269–287, 2005. [received the "Best Paper Award 2005 of Japanese SIAM"]. (PDF)
• T. Ota, S. Oishi, T. Ogita, and S.M. Rump. Verified Solutions of Extremely Ill-conditioned Linear Systems. Nihon Shimyureshon Gakkai Taikai Happyo Ronbunshu, 24:225–228, 2005.
• K. Ozaki, T. Ogita, S. Miyajima, S. Oishi, and S.M. Rump. Componentwise Verified Solutions of Linear System Suited for Java. In Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications, Bruge, Belgium, October 18–21, pages 749–752, 2005. (PDF)
• S.M. Rump. Computer-assisted proofs and Self-Validating Methods. In B. Einarsson, editor, Handbook on Accuracy and Reliability in Scientific Computation, pages 195–240. SIAM, 2005. (PDF)
• S.M. Rump. High Precision Evaluation of Nonlinear Functions. In Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications, Bruge, Belgium, October 18–21, pages 733–736, 2005. (PDF)
• S.M. Rump. INTLAB - Interval Laboratory, a Matlab toolbox for verified computations, Version 5.1, 2005. http://www.ti3.tu-harburg.de/intlab/.
• T. Ogita, S.M. Rump, and S. Oishi. Accurate Sum and Dot Product with Applications. Proceedings of 2004 IEEE International Symposium on Computer Aided Control Systems Design, Taipei, pages 152–155, 2004. (PDF)
• T. Ota, S. Oishi, T. Ogita, and S.M. Rump. Numerical Verification Method for Simultaneous Linear Equations using Accurate Dot Product Calculation Algorithm. Nihon Shimyureshon Gakkai Taikai Happyo Ronbunshu, 23:345–348, 2004.
• S.M. Rump. Computer-Assisted Proofs I. Bulletin of the Japan Society for Industrial and Applied Mathematics (Bull. JSIAM), 14(3):2–11, 2004. translated by T. Ogita. (PDF)
• S.M. Rump. Computer-Assisted Proofs II. Bulletin of the Japan Society for Industrial and Applied Mathematics (Bull. JSIAM), 14(4):44–57, 2004. translated by T. Ogita. (PDF)
• S.M. Rump and J. Zemke. On eigenvector bounds. BIT Numerical Mathematics, 43:823–837, 2004. (PDF)
• A.C. Hailer and S.M. Rump. Hedge-Effektivität: Lösung des Problems der kleinen Zahlen. (Hedge Accounting nach FAS 133 bzw. IAS 39. Zeitschrift für das gesamte Kreditwesen, 56(2003)(11):599–603, 2003.
• S.M. Rump. Algorithms for Computing Validated Results. In J. Grabmeier, E. Kaltofen, and V. Weispfennig, editors, Computer Algebra Handbook, chapter 2.12.2, pages 110–112. Springer, 2003. (PDF)
• S.M. Rump. On Nishi's conditions for the Omega-property. IEICE Trans. Fundamentals Communications Electronics Information and Systems, E86(9):2357–2359, 2003. (PDF)
• S.M. Rump. On P-Matrices. Linear Algebra and its Applications (LAA), 363:237–250, 2003. (PDF)
• S.M. Rump. Optimal scaling for p-norms and componentwise distance to singularity. IMA Journal of Numerical Analysis (IMAJNA), 23:1–9, 2003. (PDF)
• S.M. Rump. Perron-Frobenius Theory for Complex Matrices. Linear Algebra and its Applications (LAA), 363:251–273, 2003. (PDF)
• S.M. Rump. Structured Perturbations Part I: Normwise Distances. SIAM J. Matrix Anal. Appl. (SIMAX), 25(1):1–30, 2003. (PDF)
• S.M. Rump. Structured Perturbations Part II: Componentwise Distances. SIAM J. Matrix Anal. Appl. (SIMAX), 25(1):31–56, 2003. (PDF)
• S.M. Rump. Ten methods to bound multiple roots of polynomials. J. Comput. Appl. Math. (JCAM), 156:403–432, 2003. (PDF)
• S. Oishi and S.M. Rump. Fast verification of solutions of matrix equations. Numer. Math., 90(4):755–773, 2002. (PDF)
• S.M. Rump. Variational characterizations of the sign-real and the sign-complex spectral radius. Electronic Journal of Linear Algebra (ELA), 9:112–117, 2002. (PDF)
• S.M. Rump. Computational Error Bounds for Multiple or Nearly Multiple Eigenvalues. Linear Algebra and its Applications (LAA), 324:209–226, 2001. (PDF)
• S.M. Rump. Conservatism of the circle criterion - solution of a problem posed by A. Megretski. IEEE Trans. Automatic Control, 46(10):1605–1608, 2001. (PDF)
• S.M. Rump. Fast verification algorithms in Matlab. In G. Alefeld, J. Rohn, S. Rump, and T. Yamamoto, editors, Symbolic Algebraic Methods and Verification Methods, pages 209–226. Springer Mathematics, 2001. (PDF)
• S.M. Rump. Interval Arithmetic and Fuzzy Logic. In Proc. of the International NAISO congress on Information Science Innovations (ISI'2001), Dubai, pages 379–386, 2001.
• S.M. Rump. Rigorous and portable standard functions. BIT Numerical Mathematics, 41(3):540–562, 2001. (PDF)
• S.M. Rump. Self-validating methods. Linear Algebra and its Applications (LAA), 324:3–13, 2001. (PDF)
• S.M. Rump. A simple application of interval arithmetic. Brazilian Electronic Journal on Mathematics of Computation (BEJMC), 2, 2000. (PDF)
• S.M. Rump. Fast and parallel interval arithmetic. BIT Numerical Mathematics, 39(3):539–560, 1999. (PDF)
• S.M. Rump. Ill-conditioned Matrices are componentwise near to singularity. SIAM Review (SIREV), 41(1):102–112, 1999. (PDF)
• S.M. Rump. Ill-conditionedness need not be componentwise near to ill-posedness for least squares problems. BIT Numerical Mathematics, 39(1):143–151, 1999. (PDF)
• S.M. Rump. Interval computations with INTLAB. Brazilian Electronic Journal on Mathematics of Computation (BEJMC), 1, 1999. (PDF)
• S.M. Rump. INTLAB - INTerval LABoratory. In Tibor Csendes, editor, Developments in Reliable Computing, pages 77–104. Kluwer Academic Publishers, Dordrecht, 1999. (PDF)
• S.M. Rump. Verified Solution of Large Linear and Nonlinear Systems. In H. Bulgak and C. Zenger, editors, Error Control and adaptivity in Scientific Computing, pages 279–298. Kluwer Academic Publishers, 1999. (PDF)
• D. Dennis, V. Kreinovich, and S.M. Rump. Intervals and the Origins of Calculus. Reliable Computing, 4(2):191–197, 1998. (PDF)
• S.M. Rump. A Note on Epsilon-Inflation. Reliable Computing, 4:371–375, 1998. (PDF)
• S.M. Rump. INTLAB - Interval Laboratory, Version 1, 1998.
• S.M. Rump. Structured Perturbations and Symmetric Matrices. Linear Algebra and its Applications (LAA), 278:121–132, 1998. (PDF)
• S.M. Rump. The sign-real spectral radius and cycle products. Linear Algebra and its Applications (LAA), 279:177–180, 1998. (PDF)
• S.M. Rump. Almost Sharp Bounds for the Componentwise Distance to the Nearest Singular Matrix. Linear and Multilinear Algebra (LAMA), 42:93–107, 1997. (PDF)
• S.M. Rump. Bounds for the Componentwise Distance to the Nearest Singular Matrix. SIAM J. Matrix Anal. Appl. (SIMAX), 18(1):83–103, 1997. (PDF)
• S.M. Rump. HARDY - High-Accuracy Arithmetic Applied to Dimensionl Metrology. In Proceedings of the 4th German-Brazilian Workshop on Information Technology, pages 9–12, Berlin, 1997.
• S.M. Rump. Inclusion of zeros of nowhere differentiable n-dimensional functions. Reliable Computing, 3(1):5–16, 1997. (PDF)
• S.M. Rump. Theorems of Perron-Frobenius type for matrices without sign restrictions. Linear Algebra and its Applications (LAA), 266:1–42, 1997. (PDF)
• R. Lindemann and S.M. Rump. COX - C with Operator eXtension. Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 76, Suppl. 1:53–56, 1996.
• W. Mackens and S.M. Rump. Software Engineering im Scientific Computing. Vieweg Verlag, 1996.
• S.M. Rump. Expansion and Estimation of the Range of Nonlinear Functions. Math. Comput., 65(216):1503–1512, 1996. (PDF)
• S.M. Rump. Improved Iteration Schemes for Validation Algorithms for Dense and Sparse Nonlinear Systems. Computing, 57(1):77–84, 1996. (PDF)
• S.M. Rump. The distance between regularity and strong regularity. In G. Alefeld, A. Frommer, and B. Lang, editors, Scientific Computing and Validated Numerics, volume 90 of Mathematical Research, pages 105–117. Akademie Verlag, 1996. (PDF)
• S.M. Rump. Verified Computation of the Solution of Large Sparse Linear Systems. Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 75:S439–S442, 1995. (PDF)
• S.M. Rump. Verified Solution of Large Systems and Global Optimization Problems. J. Comput. Appl. Math. (JCAM), 60:201–218, 1995. (PDF)
• C. Jansson and S.M. Rump. Algorithmen mit Ergebnisverifikation — einige Bemerkungen zu neueren Entwicklungen. In Jahrbuch Überblicke Mathematik, pages 47–73. Vieweg, 1994. (PDF)
• C. Jansson and S.M. Rump. Self-Validating Methods - Some Recent Developements. In E. Schock, editor, Beiträge zur Angewandten Analysis und Informatik, pages 148–170. Shaker Verlag, 1994. (PDF)
• S.M. Rump. Verification Methods for Dense and Sparse Systems of Equations. In J. Herzberger, editor, Topics in Validated Computations — Studies in Computational Mathematics, pages 63–136, Elsevier, Amsterdam, 1994. (PDF)
• D. Claudio and S.M. Rump. GANA - Guaranteed Accuracy for Numerical Algorithms. In Proceedings of the German Brazilian Workshop on Information Technology, Berlin, 1993.
• S.M. Rump. Validated Solution of Large Linear Systems. In R. Albrecht, G. Alefeld, and H.J. Stetter, editors, Validation numerics: theory and applications, volume 9 of Computing Supplementum, pages 191–212. Springer, 1993. (PDF)
• S.M. Rump. Zur Außen- und Inneneinschließung von Eigenwerten bei toleranzbehafteten Matrizen. Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 73(7-8):T861–T863, 1993. (PDF)
• D.M. Claudio and S.M. Rump. Inclusion methods for real and complex functions in one variable. Technical Report 92.5, Forschungsschwerpunkt Informations- und Kommunikationstechnik, TU Hamburg-Harburg, 1992.
• S.M. Rump. Accuracy Control and Estimation, Self-Validating Systems and Software Environments for Scientific Computation. In P. Gaffney and E. Houstis, editors, IFIP Transactions on Programming Environments for High-Level Scientific Problem Solving, pages 49–56. North-Holland, Amsterdam, 1992.
• S.M. Rump. Inclusion of the Solution for Large Linear Systems with M-Matrix. In L. Atanassova and J. Herzberger, editors, Computer Arithmetic and Enclosure Methods, pages 339–350. Elsevier Science Publisher B.V., 1992.
• S.M. Rump. Inclusion of the Solution of Large Linear Systems with M-Matrix. Interval Computations, 1(3):22–43, 1992.
• S.M. Rump. On the Solution of Interval Linear Systems. Computing, 47:337–353, 1992. (PDF)
• S.M. Rump. Recent Results in Interval Mathematics. In Proc. 5th International Conference on Scientific Computing, Benin City, 1992.
• D. Husung and S.M. Rump. ABACUS, Sprachbeschreibung. In L. Atanassova et al., editor, Computer arithmetic and enclosure methods: Proceedings of the Third International IMACS-GAMM Symposium on Computer Arithmetic and Scientific Computing (SCAN-91), Oldenburg, Germany, 1 - 4 October 1991, Dublin, 1991.
• C. Jansson and S.M. Rump. Rigorous Solution of Linear Programming Problems with Uncertain Data. ZOR — Methods and Models of Operations Research, 35:87–111, 1991. (PDF)
• S.M. Rump. A Class of Arbitrarily Ill-conditioned Floating-Point Matrices. SIAM J. Matrix Anal. Appl. (SIMAX), 12(4):645–653, 1991. (PDF)
• S.M. Rump. Convergence Properties of Iterations Using Sets. Wissenschaftliche Zeitschrift, TU Leipzig, 15(6):427–432, 1991. (PDF)
• S.M. Rump. Estimation of the Sensitivity of Linear and Nonlinear Algebraic Problems. Linear Algebra and its Applications (LAA), 153:1–34, 1991. (PDF)
• C. Jansson and S.M. Rump. Rigorous Sensitivity Analysis for Systems of Linear Equations and Linear Programming Problems. Methods of Operation Research, 62:459–473, 1990.
• S.M. Rump. ACRITH - CALCULUS - TPX - Programmierwerkzeuge für wissenschaftliches Rechnen. In Tagungsband Wissenschaftliches Forum, Hamburg, 1990.
• S.M. Rump. Approximate inverses of almost singular matrices still contain useful information. Technical Report 90.1, Forschungsschwerpunkt Informations- und Kommunikationstechnik, TU Hamburg-Harburg, 1990. (PDF)
• S.M. Rump. Rigorous Sensitivity Analysis for Systems of Linear and Nonlinear Equations. Math. Comput., 54(10):721–736, 1990. (PDF)
• D. Husung and S.M. Rump. ABACUS. In Proceedings SCAN '89, Tagung ''Wissenschaftliches Rechnen und Programmiersprachen'', pages 52–53, Basel, 1989.
• S.M. Rump. CALCULUS. In U. Kulisch, editor, Wissenschaftliches Rechnen mit Ergebnisverifikation, pages 85–99. Vieweg und Akademie Verlag, Berlin, 1989.
• S.M. Rump. Guaranteed Inclusions for the Complex Generalized Eigenproblem. Computing, 42:225–238, 1989. (PDF)
• S.M. Rump. Lineare Probleme. In U. Kulisch, editor, Wissenschaftliches Rechnen mit Ergebnisverifikation, pages 119–127. Vieweg und Akademie Verlag, Berlin, 1989.
• T. Merschen and S.M. Rump. Genaues Rechnen. Technical report, Fachbereich Lehre und Forschung, IBM, 1988.
• S.M. Rump. Algebraic Computation, Numerical Computation, and Verified Inclusions. In R. Janßen, editor, Trends in Computer Algebra, pages 177–197. Lecture Notes in Computer Science 296, 1988.
• S.M. Rump. Algorithms for Verified Inclusions - Theory and Practice. In R.E. Moore, editor, Reliability in Computing, volume 19 of Perspectives in Computing, pages 109–126. Academic Press, 1988. (PDF)
• S.M. Rump. Garantiert richtige Ergebnisse auf Rechenanlagen (ACRITH). In Tagungsband Wissenschaftliches Forum, München, 1988.
• U. Allendörfer, H. Böhm, G. Bohlender, K. Grüner, E. Kaucher, R. Kirchner, R. Klatte, U. Kulisch, M. Neaga, L.B. Rall, S.M. Rump, R. Saier, L. Schindele, Ch. Ullrich, H.W. Wippermann, and J. Wolff von Gudenberg. PASCAL-SC: A PASCAL Extension for Scientific Computation, Information Manual and Floppy Disks, Version IBM PC. B.G. Teubner und John Wiley & Sons, Stuttgart und Chichester, 1987.
• U. Allendörfer, H. Böhm, G. Bohlender, K. Grüner, E. Kaucher, R. Kirchner, R. Klatte, U. Kulisch, M. Neaga, L.B. Rall, S.M. Rump, R. Saier, L. Schindele, Ch. Ullrich, H.W. Wippermann, and J. Wolff von Gudenberg. PASCAL-SC: A PASCAL Extension for Scientific Computation for the ATARI ST, Information Manual and Floppy Disks. B.G. Teubner, Stuttgart, 1987.
• J.H. Bleher, S.M. Rump, U. Kulisch, M. Metzger, C. Ullrich, and W. Walter. FORTRAN-SC: A Study of a FORTRAN Extension for Engineering/Scientific Computation with Access to ACRITH. Computing, 39:93–110, 1987.
• S.M. Rump. Introduction to ARCRITH - Accurate Scientific Algorithms. In E. Kaucher, U. Kulisch, and Ch. Ullrich, editors, Computerarithmetic, pages 296–369. B.G. Teubner, 1987.
• S.M. Rump. Numerische Software mit automatischer Verifikation. Technical report, Universität Duisburg, 1987.
• S.M. Rump. Solution of Linear Systems with Verified Accuracy. Applied Numerical Mathematics, 3:233–241, 1987.
• S.M. Rump, H. Böhm, and G. Schuhmacher. E-Methods for Nonlinear Problems. In E. Kaucher, U. Kulisch, and Ch. Ullrich, editors, Computerarithmetic, pages 59–80. B.G. Teubner, 1987.
• B. Buchberger, M. Feilmeier, M. Kratz, U. Kulisch, B. Kutzler, and S.M. Rump. Rechnerorientierte Verfahren. B.G. Teubner, 1986.
• U. Kulisch and S.M. Rump. Rechnerorientierte Verfahren, chapter Rechnerarithmetik und die Behandlung Algebraischer Probleme, pages 213–281. Vieweg+Teubner Verlag, Wiesbaden, 1986. (PDF)
• M. Mascagni, W.L. Miranker, and S.M. Rump. Case Studies for Augmented Floating-Point Arithmetic. In W.L. Miranker and R. Toupin, editors, Accurate Scientific Computations, volume 235 of Lecture Notes in Computer Science, pages 86–118. Springer, 1986.
• S.M. Rump. Demonstration of ACRITH - An advanced package for scientific computation. In Proceedings of the 11th IMACS World Congress, volume 85 of IMACS Transactions on Scientific Computation, pages 331–334, Oslo, Norway, 1986.
• S.M. Rump. New Results on Verified Inclusions. In W.L. Miranker and R. Toupin, editors, Accurate Scientific Computations, pages 31–69. Springer Lecture Notes in Computer Science 235, 1986. (PDF)
• S.M. Rump. Properties of a Higher Order Computer Arithmetic. In Proceedings of the 11th IMACS World Congress, volume 85 of IMACS Transactions on Scientific Computation, pages 163–165, Oslo, Norway, 1986.
• S.M. Rump. Sichere Ergebnisse auf Rechenanlagen. Informatik Spektrum, 9(3):174–183, 1986. (PDF)
• D.K. Unkauf, A.T. Gerlicher, S.M. Rump, and J.H. Bleher. Verfahren und Schaltungsanordnung zur Addition von Gleitkommazahlen - Patentanmeldung. Technical report, IBM, 1986.
• J.H. Bleher, A.E. Röder, and S.M. Rump. High Accuracy Arithmetic - ACRITH. In Proceedings of the SHARE 64 Meeting, pages 318–321, Los Angeles, California, 1985.
• S.M. Rump. ACRITH - High Accuracy Arithmetic Subroutine Library. In Proceedings of EUROCAL'85, European Conference on Computer Algebra, Linz, Austria, volume 203 of Lecture Notes in Computer Science. Springer, 1985.
• S.M. Rump. ACRITH - Numerical Methods with Verified Accuracy. In Proceedings of the Congress on Numerical Fluid Dynamics, pages 82–92, Tokyo, Japan, 1985.
• S.M. Rump. Higher Order Computer Arithmetic. In Proceedings of the ARITH 7 Conference on Computer Arithmetic, pages 302–308, Urbana, Illinois, 1985.
• S.M. Rump. Numerical Methods with Automatic Verification. In Proceedings of EUROCAL'85, European Conference on Computer Algebra, volume 203 of Lecture Notes in Computer Science, pages 26–27, Linz, Austria, 1985.
• J.H. Bleher, A.E. Röder, and S.M. Rump. ACRITH: High Accuracy Arithmetic - An Advanced Tool for Scientific Computation. In Proceedings of the SHARE 63 Meeting, pages 1–23, Miami, 1984. (PDF)
• G. Bohlender, H. Böhm, K. Grüner, E. Kaucher, D. Klatte, W. Krämer, U. Kulisch, W.L. Miranker, Ch. Ullrich, S.M. Rump, and J. Wolff v. Gudenberg. Arithmetic Specification in FORTRAN 8x. In B. Ford, J.C. Rault, and F. Thomasset, editors, Tools, Methods and Languages for Scientific and Engineering Computation, Proc. int. Conf., pages 213–243, Paris, 1984.
• S.M. Rump. Naive and Non-naive Interval Arithmetic in Scientific Computation. In Proceedings of the Conference on ''Numerical Mathematics'' , pages 1–18, Sao Carlos, Brazil, 1984.
• S.M. Rump. Solution of Linear and Nonlinear Algebraic Problems with Sharp Guaranteed Bounds. Comput. Suppl., 5:147–168, 1984. (PDF)
• S.M. Rump. The use of interval arithmetic in scienfific computation. In Proceedings ''First International Conference on Computers and Applications'' , pages 719–724, Beijing, China, 1984.
• W.L. Miranker and S.M. Rump. Case Studies for ACRITH, 1. Ill posed problems and 2. Stiff Differenctial Systems. Technical report, IBM Thomas J. Watson Research Center, Yorktown Heights, New York, 1983.
• S.M. Rump. How Reliable are Results of Computers?, Translation of ``Wie zuverlässig sind die Ergebnisse unserer Rechenanlagen?''. Jahrbuch Überblicke Mathematik, pages 163–168, 1983. (PDF)
• S.M. Rump. Solving Algebraic Problems with High Accuracy. Habilitationsschrift. In U.W. Kulisch and W.L. Miranker, editors, A New Approach to Scientific Computation, pages 51–120. Academic Press, New York, 1983. (PDF)
• S.M. Rump. Wie zuverlässig sind die Ergebnisse unserer Rechenanlagen? Jahrbuch Überblicke Mathematik, pages 163–168, 1983. (PDF)
• S.M. Rump and H. Böhm. Least significant bit evaluation for arithmetic expressions. Computing, 30:189–199, 1983. (PDF)
• U. Kulisch, S.M. Rump, and J.W. von Gudenberg. Accuracy of the IBM 370 floating-point arithmetic and possible improvements. Technical report, IBM, 1982.
• S.M. Rump. Rechnervorführung, Pakete für Standardprobleme der Numerik. In U.W. Kulisch and Ch. Ullrich, editors, ''Wissenschaftliches Rechnen und Programmiersprachen'', pages 29–50. B.G. Teubner, 1982.
• S.M. Rump. Solving Non-Linear Systems with Least Significant Bit Accuracy. Computing, 29:183–200, 1982. (PDF)
• G. Bohlender, K. Grüner, E. Kaucher, D. Klatte, W. Krämer, U. Kulisch, W.L. Miranker, Ch. Ullrich, S.M. Rump, and J. Wolff v. Gudenberg. PASCAL-SC - A PASCAL for Contemporary Scientific Computation. Technical report, IBM, Yorktown Heights, 1981.
• S.M. Rump. Exakte Fehlerschranken für Eigenwerte und Eigenvektoren. Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 61(5):T311–313, 1981.
• S.M. Rump. Kleine, exakte Fehlerschranken für die Lösung linearer Gleichungssysteme. Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 61(5):T313–315, 1981.
• E. Kaucher and S.M. Rump. Generalized Iteration Methods for Bounds of the Solution of Fixed-Point Operator Equations. Computing, 24:131–137, 1980.
• E. Kaucher and S.M. Rump. Small bounds for the Solution of Systems of Linear Equations. Comput. Suppl., 2:157–164, 1980. (PDF)
• S.M. Rump. Kleine Fehlerschranken bei Matrixproblemen. PhD thesis, Universität Karlsruhe, 1980. (PDF)
• S.M. Rump. Notiz zur Genauigkeit der Arithmetik in Rechenanlagen. Elektron. Rechenanlagen, 22(5):243–244, 1980. (PDF)
• S.M. Rump. Zur Rückführung nicht mehr benötigten Speicherplatzes in PASCAL. Elektron. Rechenanlagen, 22:55–62, 1980.
• S.M. Rump. Polynomial Minimum Root Separation. Math. Comput., 33(145):327–336, 1979. (PDF)
• S.M. Rump. Is at least one of k greater eqal 2 consecutive positive rational integers prime to all others? Technical report, Institut für Angewandte Mathematik, Universität Karlsruhe, 1978.
• S.M. Rump. Real Root Isolation for Algebraic Polynomials. ACM SIGSAM Bulletin, 11(2):327–336, 1977. (PDF)
• S.M. Rump. Ein Algorithmus zur Isolierung der reellen Nullstellen eines Polynoms mit algebraischen Koeffizienten, Rechenzeitanalyse und Implementierung. Master's thesis, Universität Kaiserslautern, 1976.
• S.M. Rump. Isolierung der reellen Nullstellen algebraischer Polynome. Technical Report 10, Arbeitsgruppe Algebra, Universität Kaiserslautern, 1976.
• S.M. Rump. On the Sign of a Real Algebraic Number. In Proceedings of the 1976 ACM Symposium on Symbolic and Algebraic Computation, pages 238–241, New York, 1976. (PDF)