Siegfried M. Rump

Publication Activity (10 Years)

Years Active: 1976-2023
Publications (10 Years): 15

Top Topics

Condition Numbers

Top Venues

J. Comput. Appl. Math.

SIAM J. Matrix Anal. Appl.

ACM Trans. Math. Softw.

Publications

Siegfried M. Rump, Marko Lange
Fast computation of error bounds for all eigenpairs of a Hermitian and all singular pairs of a rectangular matrix with emphasis on eigen- and singular value clusters. J. Comput. Appl. Math. 434 (2023)
Siegfried M. Rump
base-β Arithmetic Implemented in Binary. ACM Trans. Math. Softw. 49 (4) (2023)
Manuel Radons, Siegfried M. Rump
Convergence results for some piecewise linear solvers. Optim. Lett. 16 (6) (2022)
Siegfried M. Rump
Verified Error Bounds for All Eigenvalues and Eigenvectors of a Matrix. SIAM J. Matrix Anal. Appl. 43 (4) (2022)
Mitsuhiro T. Nakao, Takeshi Ogita, Siegfried M. Rump
Foreword. J. Comput. Appl. Math. 382 (2021)
Atsushi Minamihata, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi
Modified error bounds for approximate solutions of dense linear systems. J. Comput. Appl. Math. 369 (2020)
Manuel Radons, Siegfried M. Rump
Convergence results for some piecewise linear solvers. CoRR (2020)
Marko Lange, Siegfried M. Rump
Faithfully Rounded Floating-point Computations. ACM Trans. Math. Softw. 46 (3) (2020)
Siegfried M. Rump
Verified bounds for the determinant of real or complex point or interval matrices. J. Comput. Appl. Math. 372 (2020)
Marko Lange, Siegfried M. Rump
Sharp estimates for perturbation errors in summations. Math. Comput. 88 (315) (2019)
Siegfried M. Rump
Error Bounds for Computer Arithmetics. ARITH (2019)
Andreas Griewank, Andrea Walther, Koichi Kubota, Siegfried M. Rump
Piecewise smooth system and optimization with piecewise linearization via algorithmic differentiation (NII Shonan Meeting 2018-9). NII Shonan Meet. Rep. 2018 (2018)
Siegfried M. Rump
Mathematically rigorous global optimization in floating-point arithmetic. Optim. Methods Softw. 33 (4-6) (2018)
Claude-Pierre Jeannerod, Siegfried M. Rump
On relative errors of floating-point operations: Optimal bounds and applications. Math. Comput. 87 (310) (2018)
Siegfried M. Rump
. ACM Trans. Math. Softw. 43 (3) (2017)
Siegfried M. Rump
The Componentwise Structured and Unstructured Backward Errors Can be Arbitrarily Far Apart. SIAM J. Matrix Anal. Appl. 36 (2) (2015)
Siegfried M. Rump, Claude-Pierre Jeannerod
Improved Backward Error Bounds for LU and Cholesky Factorizations. SIAM J. Matrix Anal. Appl. 35 (2) (2014)
Siegfried M. Rump
Verified Bounds for the p-Norm Condition Number. Reliab. Comput. 20 (2014)
Siegfried M. Rump
Improved componentwise verified error bounds for least squares problems and underdetermined linear systems. Numer. Algorithms 66 (2) (2014)
Claude-Pierre Jeannerod, Siegfried M. Rump
Improved Error Bounds for Inner Products in Floating-Point Arithmetic. SIAM J. Matrix Anal. Appl. 34 (2) (2013)
Siegfried M. Rump
Accurate solution of dense linear systems, Part II: Algorithms using directed rounding. J. Comput. Appl. Math. 242 (2013)
Siegfried M. Rump
Accurate solution of dense linear systems, part I: Algorithms in rounding to nearest. J. Comput. Appl. Math. 242 (2013)
Tetsuo Nishi, Siegfried M. Rump, Shin'ichi Oishi
A consideration on the condition number of extremely ill-conditioned matrices. ECCTD (2013)
Siegfried M. Rump
Verified Bounds for Least Squares Problems and Underdetermined Linear Systems. SIAM J. Matrix Anal. Appl. 33 (1) (2012)
Katsuhisa Ozaki, Takeshi Ogita, Shin'ichi Oishi, Siegfried M. Rump
Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications. Numer. Algorithms 59 (1) (2012)
Katsuhisa Ozaki, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi
Fast algorithms for floating-point interval matrix multiplication. J. Comput. Appl. Math. 236 (7) (2012)
Siegfried M. Rump
Fast interval matrix multiplication. Numer. Algorithms 61 (1) (2012)
Siegfried M. Rump
Verification methods: rigorous results using floating-point arithmetic. ISSAC (2010)
Siegfried M. Rump, Stef Graillat
Verified error bounds for multiple roots of systems of nonlinear equations. Numer. Algorithms 54 (3) (2010)
Shinya Miyajima, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi
Fast Verification for All Eigenpairs in Symmetric Positive Definite Generalized Eigenvalue Problems. Reliab. Comput. 14 (2010)
Siegfried M. Rump
Accurate and Reliable Computing in Floating-Point Arithmetic. ICMS (2010)
Siegfried M. Rump
Verification methods: Rigorous results using floating-point arithmetic. Acta Numer. 19 (2010)
Siegfried M. Rump
Ultimately Fast Accurate Summation. SIAM J. Sci. Comput. 31 (5) (2009)
B. Malcolm Brown, Erich Kaltofen, Shin'ichi Oishi, Siegfried M. Rump
09471 Abstracts Collection - Computer-assisted proofs - tools, methods and applications. Computer-assisted proofs - tools, methods and applications (2009)
B. Malcolm Brown, Erich Kaltofen, Shin'ichi Oishi, Siegfried M. Rump
09471 Executive Summary - Computer-assisted proofs - tools, methods and applications. Computer-assisted proofs - tools, methods and applications (2009)
Siegfried M. Rump, Takeshi Ogita, Shin'ichi Oishi
Accurate Floating-Point Summation Part I: Faithful Rounding. SIAM J. Sci. Comput. 31 (1) (2008)
Naoya Yamanaka, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi
A parallel algorithm for accurate dot product. Parallel Comput. 34 (6-8) (2008)
Siegfried M. Rump, Takeshi Ogita, Shin'ichi Oishi
Accurate Floating-Point Summation Part II: Sign, K-Fold Faithful and Rounding to Nearest. SIAM J. Sci. Comput. 31 (2) (2008)
Vladik Kreinovich, Siegfried M. Rump
Towards Optimal Use of Multi-Precision Arithmetic: A Remark. Reliab. Comput. 12 (5) (2006)
Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi
Accurate Sum and Dot Product. SIAM J. Sci. Comput. 26 (6) (2005)
Bruno Buchberger, Christian Jansson, Shin'ichi Oishi, Michael Plum, Siegfried M. Rump
05391 Executive Summary - Numerical and Algebraic Algorithms and Computer-assisted Proofs. Algebraic and Numerical Algorithms and Computer-assisted Proofs (2005)
Bruno Buchberger, Shin'ichi Oishi, Michael Plum, Siegfried M. Rump
05391 Abstracts Collection - Algebraic and Numerical Algorithms and Computer-assisted Proofs. Algebraic and Numerical Algorithms and Computer-assisted Proofs (2005)
Siegfried M. Rump
Structured Perturbations Part I: Normwise Distances. SIAM J. Matrix Anal. Appl. 25 (1) (2003)
Siegfried M. Rump
On Nishi's Conditions for Ω-Property. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. (9) (2003)
Siegfried M. Rump
Structured Perturbations Part II: Componentwise Distances. SIAM J. Matrix Anal. Appl. 25 (1) (2003)
Shin'ichi Oishi, Siegfried M. Rump
Fast verification of solutions of matrix equations. Numerische Mathematik 90 (4) (2002)
Siegfried M. Rump
Conservatism of the circle criterion-solution of a problem posed by A. Megretski. IEEE Trans. Autom. Control. 46 (10) (2001)
Siegfried M. Rump
Ill-Conditioned Matrices Are Componentwise Near to Singularity. SIAM Rev. 41 (1) (1999)
Siegfried M. Rump
INTLAB - INTerval LABoratory. SCAN (1998)
David Dennis, Vladik Kreinovich, Siegfried M. Rump
Intervals and the Origins of Calculus. Reliab. Comput. 4 (2) (1998)
Siegfried M. Rump
A Note on Epsilon-Inflation. Reliab. Comput. 4 (4) (1998)
Siegfried M. Rump
Bounds for the Componentwise Distance to the Nearest Singular Matrix. SIAM J. Matrix Anal. Appl. 18 (1) (1997)
Siegfried M. Rump
Inclusion of Zeros of Nowhere Differentiable n-Dimensional Functions. Reliab. Comput. 3 (1) (1997)
Siegfried M. Rump
Improved Iteration Schemes for Validation Algorithms for DenseSparse Nonlinear Systems. Computing 57 (1) (1996)
Siegfried M. Rump
Expansion and estimation of the range of nonlinear functions. Math. Comput. 65 (216) (1996)
Dalcidio Moraes Claudio, Siegfried M. Rump
Inclusion methods for real and complex functions in one variable. RITA 2 (1) (1995)
Siegfried M. Rump
On the solution of interval linear systems. Computing 47 (3-4) (1992)
Siegfried M. Rump
Accuracy Control and Estimation, Self-Validating Systems and Software Environments for Scientific Computation. Programming Environments for High-Level Scientific Problem Solving (1991)
Christian Jansson, Siegfried M. Rump
Rigorous solution of linear programming problems with uncertain data. ZOR Methods Model. Oper. Res. 35 (2) (1991)
Siegfried M. Rump
Guaranteed inclusions for the complex generalized eigenproblem. Computing 42 (2-3) (1989)
J. Hartmut Bleher, Siegfried M. Rump, Ulrich W. Kulisch, M. Metzger, Christian P. Ullrich, W. Walter
FORTRAN-SC a study of a FORTRAN extension for engineering/scientific computation with access to ACRITH. Computing 39 (2) (1987)
Siegfried M. Rump
Algebraic Computation, Numerical Computation and Verified Inclusions. Trends in Computer Algebra (1987)
Siegfried M. Rump
Sichere Ergebnisse auf Rechenanlagen. Inform. Spektrum 9 (3) (1986)
Willard L. Miranker, Michael Mascagni, Siegfried M. Rump
Case Studies for Augmented Floating-Point. Accurate Scientific Computations (1985)
Siegfried M. Rump
New Results on Verified Inclusions. Accurate Scientific Computations (1985)
Siegfried M. Rump
Higher Order Computer Arithmetic. IEEE Symposium on Computer Arithmetic (1985)
J. Hartmut Bleher, A. E. Roeder, Siegfried M. Rump
ACRITH: High-Accuracy Arithmetic an advanced tool for numerical computation. IEEE Symposium on Computer Arithmetic (1985)
Siegfried M. Rump
ACRITH - High Accuracy Arithmetic Subroutine Library. European Conference on Computer Algebra (2) (1985)
Siegfried M. Rump
Numerical Methods with Automatic Verification. European Conference on Computer Algebra (2) (1985)
Siegfried M. Rump
Mathematik auf dem Rechner. Elektron. Rechenanlagen 25 (6) (1983)
Siegfried M. Rump, Harald Böhm
Least significant bit evaluation of arithmetic expressions in single-precision. Computing 30 (3) (1983)
Siegfried M. Rump
Rechnervorführung, Pakete für Standardprobleme der Numerik. Wissenschaftliches Rechnen und Programmiersprachen (1982)
Siegfried M. Rump
Solving nonlinear systems with least significant bit accuracy. Computing 29 (3) (1982)
Siegfried M. Rump
Lösung linearer und nichtlinearer Gleichungssysteme mit maximaler Genauigkeit. Wissenschaftliches Rechnen und Programmiersprachen (1982)
Edgar Kaucher, Siegfried M. Rump
E-methods for fixed point equations f(x)=x. Computing 28 (1) (1982)
Siegfried M. Rump
Computer und Rechengenauigkeit. Elektron. Rechenanlagen 24 (6) (1982)
Siegfried M. Rump
Solving Algebraic Problems with High Accuracy. IMACS World Congress (1982)
Siegfried M. Rump
Notiz zur Genauigkeit der Arithmetik in Rechenanlagen. Elektron. Rechenanlagen 22 (5) (1980)
Edgar Kaucher, Siegfried M. Rump
Generalized iteration methods for bounds of the solution of fixed point operator-equations. Computing 24 (2-3) (1980)
Siegfried M. Rump
Zur Rückführung nicht mehr benötigten Speicherplatzes in PASCAL. Elektron. Rechenanlagen 22 (2) (1980)
Siegfried M. Rump
Real root isolation for algebraic polynomials. SIGSAM Bull. 11 (2) (1977)
Siegfried M. Rump
On the sign of a real algebraic number. SYMSACC (1976)