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Siegfried M. Rump
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- affiliation: Hamburg-Harburg University of Technology, Institute for Reliable Computing, Germany
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2020 – today
- 2023
- [j59]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: 115332 (2023) - [j58]Siegfried M. Rump
IEEE-754 Precision-p base-β Arithmetic Implemented in Binary. ACM Trans. Math. Softw. 49(4): 32:1-32:21 (2023) - 2022
- [j57]Manuel Radons
Convergence results for some piecewise linear solvers. Optim. Lett. 16(6): 1663-1673 (2022) - [j56]Siegfried M. Rump
Verified Error Bounds for All Eigenvalues and Eigenvectors of a Matrix. SIAM J. Matrix Anal. Appl. 43(4): 1736-1754 (2022) - 2021
- [j55]Mitsuhiro T. Nakao, Takeshi Ogita, Siegfried M. Rump
Foreword. J. Comput. Appl. Math. 382: 113078 (2021) - 2020
- [j54]Atsushi Minamihata, Takeshi Ogita, Siegfried M. Rump
Modified error bounds for approximate solutions of dense linear systems. J. Comput. Appl. Math. 369 (2020) - [j53]Siegfried M. Rump
Verified bounds for the determinant of real or complex point or interval matrices. J. Comput. Appl. Math. 372: 112610 (2020) - [j52]Marko Lange
Faithfully Rounded Floating-point Computations. ACM Trans. Math. Softw. 46(3): 21:1-21:20 (2020) - [i6]Manuel Radons, Siegfried M. Rump:
Convergence results for some piecewise linear solvers. CoRR abs/2012.02520 (2020)
2010 – 2019
- 2019
- [j51]Marko Lange, Siegfried M. Rump
Sharp estimates for perturbation errors in summations. Math. Comput. 88(315): 349-368 (2019) - [c17]Siegfried M. Rump
Error Bounds for Computer Arithmetics. ARITH 2019: 1-14 - 2018
- [j50]Claude-Pierre Jeannerod, Siegfried M. Rump
On relative errors of floating-point operations: Optimal bounds and applications. Math. Comput. 87(310): 803-819 (2018) - [j49]Siegfried M. Rump
Mathematically rigorous global optimization in floating-point arithmetic. Optim. Methods Softw. 33(4-6): 771-798 (2018) - [i5]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) - 2017
- [j48]Siegfried M. Rump
IEEE754 Precision-k base-β Arithmetic Inherited by Precision-m Base-β Arithmetic for k < m. ACM Trans. Math. Softw. 43(3): 20:1-20:15 (2017) - 2016
- [e4]Ilias S. Kotsireas, Siegfried M. Rump, Chee K. Yap:
Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Berlin, Germany, November 11-13, 2015, Revised Selected Papers. Lecture Notes in Computer Science 9582, Springer 2016, ISBN 978-3-319-32858-4 [contents] - 2015
- [j47]Siegfried M. Rump
The Componentwise Structured and Unstructured Backward Errors Can be Arbitrarily Far Apart. SIAM J. Matrix Anal. Appl. 36(2): 385-392 (2015) - 2014
- [j46]Siegfried M. Rump
Improved componentwise verified error bounds for least squares problems and underdetermined linear systems. Numer. Algorithms 66(2): 309-322 (2014) - [j45]Siegfried M. Rump:
Verified Bounds for the p-Norm Condition Number. Reliab. Comput. 20: 45-52 (2014) - [j44]Siegfried M. Rump
Improved Backward Error Bounds for LU and Cholesky Factorizations. SIAM J. Matrix Anal. Appl. 35(2): 684-698 (2014) - 2013
- [j43]Siegfried M. Rump
Accurate solution of dense linear systems, part I: Algorithms in rounding to nearest. J. Comput. Appl. Math. 242: 157-184 (2013) - [j42]Siegfried M. Rump
Accurate solution of dense linear systems, Part II: Algorithms using directed rounding. J. Comput. Appl. Math. 242: 185-212 (2013) - [j41]Claude-Pierre Jeannerod, Siegfried M. Rump
Improved Error Bounds for Inner Products in Floating-Point Arithmetic. SIAM J. Matrix Anal. Appl. 34(2): 338-344 (2013) - [c16]Tetsuo Nishi, Siegfried M. Rump
A consideration on the condition number of extremely ill-conditioned matrices. ECCTD 2013: 1-4 - 2012
- [j40]Katsuhisa Ozaki, Takeshi Ogita, Siegfried M. Rump
Fast algorithms for floating-point interval matrix multiplication. J. Comput. Appl. Math. 236(7): 1795-1814 (2012) - [j39]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): 95-118 (2012) - [j38]Siegfried M. Rump
Fast interval matrix multiplication. Numer. Algorithms 61(1): 1-34 (2012) - [j37]Siegfried M. Rump
Verified Bounds for Least Squares Problems and Underdetermined Linear Systems. SIAM J. Matrix Anal. Appl. 33(1): 130-148 (2012) - 2010
- [j36]Siegfried M. Rump
Verification methods: Rigorous results using floating-point arithmetic. Acta Numer. 19: 287-449 (2010) - [j35]Siegfried M. Rump
Verified error bounds for multiple roots of systems of nonlinear equations. Numer. Algorithms 54(3): 359-377 (2010) - [j34]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: 24-45 (2010) - [c15]Siegfried M. Rump
Accurate and Reliable Computing in Floating-Point Arithmetic. ICMS 2010: 105-108 - [c14]Siegfried M. Rump:
Verification methods: rigorous results using floating-point arithmetic. ISSAC 2010: 3-4
2000 – 2009
- 2009
- [j33]Siegfried M. Rump
Ultimately Fast Accurate Summation. SIAM J. Sci. Comput. 31(5): 3466-3502 (2009) - [e3]B. Malcolm Brown, Erich L. Kaltofen, Shin'ichi Oishi, Siegfried M. Rump:
Computer-assisted proofs - tools, methods and applications, 15.11. - 20.11.2009. Dagstuhl Seminar Proceedings 09471, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Germany 2009 [contents] - [i4]B. Malcolm Brown, Erich L. 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 - [i3]B. Malcolm Brown, Erich L. 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 - 2008
- [j32]Naoya Yamanaka, Takeshi Ogita, Siegfried M. Rump
A parallel algorithm for accurate dot product. Parallel Comput. 34(6-8): 392-410 (2008) - [j31]Siegfried M. Rump
Accurate Floating-Point Summation Part I: Faithful Rounding. SIAM J. Sci. Comput. 31(1): 189-224 (2008) - [j30]Siegfried M. Rump
Accurate Floating-Point Summation Part II: Sign, K-Fold Faithful and Rounding to Nearest. SIAM J. Sci. Comput. 31(2): 1269-1302 (2008) - 2006
- [j29]Vladik Kreinovich, Siegfried M. Rump
Towards Optimal Use of Multi-Precision Arithmetic: A Remark. Reliab. Comput. 12(5): 365-369 (2006) - [e2]Bruno Buchberger, Shin'ichi Oishi, Michael Plum, Siegfried M. Rump:
Algebraic and Numerical Algorithms and Computer-assisted Proofs, 25.-30. September 2005. Dagstuhl Seminar Proceedings 05391, Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany 2006 [contents] - 2005
- [j28]Takeshi Ogita, Siegfried M. Rump
Accurate Sum and Dot Product. SIAM J. Sci. Comput. 26(6): 1955-1988 (2005) - [p3]Siegfried M. Rump
10. Computer-Assisted Proofs and Self-Validating Methods. Accuracy and Reliability in Scientific Computing 2005: 195-240 - [i2]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 - [i1]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 - 2003
- [j27]Siegfried M. Rump:
On Nishi's Conditions for Ω-Property. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 86-A(9): 2357-2359 (2003) - [j26]Siegfried M. Rump
Structured Perturbations Part I: Normwise Distances. SIAM J. Matrix Anal. Appl. 25(1): 1-30 (2003) - [j25]Siegfried M. Rump
Structured Perturbations Part II: Componentwise Distances. SIAM J. Matrix Anal. Appl. 25(1): 31-56 (2003) - 2002
- [j24]Shin'ichi Oishi, Siegfried M. Rump
Fast verification of solutions of matrix equations. Numerische Mathematik 90(4): 755-773 (2002) - 2001
- [j23]Siegfried M. Rump
Conservatism of the circle criterion-solution of a problem posed by A. Megretski. IEEE Trans. Autom. Control. 46(10): 1605-1608 (2001) - [p2]Götz Alefeld, Jiri Rohn, Siegfried M. Rump, Tetsuro Yamamoto:
Introduction: Symbolic Algebraic Methods and Verification Methods. Symbolic Algebraic Methods and Verification Methods 2001: 1-2 - [p1]Siegfried M. Rump:
Fast Verification Algorithms in MATLAB. Symbolic Algebraic Methods and Verification Methods 2001: 209-226 - [e1]Götz Alefeld, Jiri Rohn, Siegfried M. Rump, Tetsuro Yamamoto:
Symbolic Algebraic Methods and Verification Methods. Springer 2001, ISBN 3-211-83593-8 [contents]
1990 – 1999
- 1999
- [j22]Siegfried M. Rump
Ill-Conditioned Matrices Are Componentwise Near to Singularity. SIAM Rev. 41(1): 102-112 (1999) - 1998
- [j21]David Dennis, Vladik Kreinovich, Siegfried M. Rump
Intervals and the Origins of Calculus. Reliab. Comput. 4(2): 191-197 (1998) - [j20]Siegfried M. Rump
A Note on Epsilon-Inflation. Reliab. Comput. 4(4): 371-375 (1998) - [c13]Siegfried M. Rump:
INTLAB - INTerval LABoratory. SCAN 1998: 77-104 - 1997
- [j19]Siegfried M. Rump
Inclusion of Zeros of Nowhere Differentiable n-Dimensional Functions. Reliab. Comput. 3(1): 5-16 (1997) - [j18]Siegfried M. Rump
Bounds for the Componentwise Distance to the Nearest Singular Matrix. SIAM J. Matrix Anal. Appl. 18(1): 83-103 (1997) - 1996
- [j17]Siegfried M. Rump
Improved Iteration Schemes for Validation Algorithms for DenseSparse Nonlinear Systems. Computing 57(1): 77-84 (1996) - [j16]Siegfried M. Rump
Expansion and estimation of the range of nonlinear functions. Math. Comput. 65(216): 1503-1512 (1996) - 1995
- [j15]Dalcidio Moraes Claudio, Siegfried M. Rump:
Inclusion methods for real and complex functions in one variable. RITA 2(1): 125-136 (1995) - 1992
- [j14]Siegfried M. Rump:
On the solution of interval linear systems. Computing 47(3-4): 337-353 (1992) - 1991
- [j13]Christian Jansson, Siegfried M. Rump
Rigorous solution of linear programming problems with uncertain data. ZOR Methods Model. Oper. Res. 35(2): 87-111 (1991) - [c12]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: 49-56
1980 – 1989
- 1989
- [j12]Siegfried M. Rump:
Guaranteed inclusions for the complex generalized eigenproblem. Computing 42(2-3): 225-238 (1989) - 1987
- [j11]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): 93-110 (1987) - [c11]Siegfried M. Rump:
Algebraic Computation, Numerical Computation and Verified Inclusions. Trends in Computer Algebra 1987: 177-197 - 1986
- [j10]Siegfried M. Rump:
Sichere Ergebnisse auf Rechenanlagen. Inform. Spektrum 9(3): 174-183 (1986) - 1985
- [c10]Siegfried M. Rump:
New Results on Verified Inclusions. Accurate Scientific Computations 1985: 31-69 - [c9]Willard L. Miranker, Michael Mascagni, Siegfried M. Rump:
Case Studies for Augmented Floating-Point. Accurate Scientific Computations 1985: 86-118 - [c8]Siegfried M. Rump
Higher Order Computer Arithmetic. IEEE Symposium on Computer Arithmetic 1985: 302-308 - [c7]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: 318-321 - [c6]Siegfried M. Rump:
Numerical Methods with Automatic Verification. European Conference on Computer Algebra (2) 1985: 318-319 - [c5]Siegfried M. Rump:
ACRITH - High Accuracy Arithmetic Subroutine Library. European Conference on Computer Algebra (2) 1985: 320-321 - 1983
- [j9]Siegfried M. Rump, Harald Böhm:
Least significant bit evaluation of arithmetic expressions in single-precision. Computing 30(3): 189-199 (1983) - [j8]Siegfried M. Rump:
Mathematik auf dem Rechner. Elektron. Rechenanlagen 25(6): 126-132 (1983) - 1982
- [j7]Edgar Kaucher, Siegfried M. Rump:
E-methods for fixed point equations f(x)=x. Computing 28(1): 31-42 (1982) - [j6]Siegfried M. Rump:
Solving nonlinear systems with least significant bit accuracy. Computing 29(3): 183-200 (1982) - [j5]Siegfried M. Rump:
Computer und Rechengenauigkeit. Elektron. Rechenanlagen 24(6): 268-277 (1982) - [c4]Siegfried M. Rump:
Rechnervorführung, Pakete für Standardprobleme der Numerik. Wissenschaftliches Rechnen und Programmiersprachen 1982: 29-50 - [c3]Siegfried M. Rump:
Lösung linearer und nichtlinearer Gleichungssysteme mit maximaler Genauigkeit. Wissenschaftliches Rechnen und Programmiersprachen 1982: 147-174 - [c2]Siegfried M. Rump:
Solving Algebraic Problems with High Accuracy. IMACS World Congress 1982: 299-300 - 1980
- [j4]Edgar Kaucher, Siegfried M. Rump:
Generalized iteration methods for bounds of the solution of fixed point operator-equations. Computing 24(2-3): 131-137 (1980) - [j3]Siegfried M. Rump:
Zur Rückführung nicht mehr benötigten Speicherplatzes in PASCAL. Elektron. Rechenanlagen 22(2): 55-62 (1980) - [j2]Siegfried M. Rump:
Notiz zur Genauigkeit der Arithmetik in Rechenanlagen. Elektron. Rechenanlagen 22(5): 243-244 (1980)
1970 – 1979
- 1977
- [j1]Siegfried M. Rump
Real root isolation for algebraic polynomials. SIGSAM Bull. 11(2): 2-3 (1977) - 1976
- [c1]Siegfried M. Rump:
On the sign of a real algebraic number. SYMSACC 1976: 238-241
Coauthor Index
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