Siegfried M. Rump - researchr alias

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Viewing Publication 1 - 84 from 84

2023

p base-β Arithmetic Implemented in BinarySiegfried M. Rump. TOMS, 49(4), December 2023. [doi]

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 clustersSiegfried M. Rump, Marko Lange. jcam, 434:115332, December 2023. [doi]

2022

Convergence results for some piecewise linear solversManuel Radons, Siegfried M. Rump. ol, 16(6):1663-1673, 2022. [doi]

Verified Error Bounds for All Eigenvalues and Eigenvectors of a MatrixSiegfried M. Rump. siammax, 43(4):1736-1754, 2022. [doi]

2021

ForewordMitsuhiro T. Nakao, Takeshi Ogita, Siegfried M. Rump. jcam, 382:113078, 2021. [doi]

2020

Faithfully Rounded Floating-point ComputationsMarko Lange, Siegfried M. Rump. TOMS, 46(3), 2020. [doi]

Modified error bounds for approximate solutions of dense linear systemsAtsushi Minamihata, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi. jcam, 369, 2020. [doi]

Verified bounds for the determinant of real or complex point or interval matricesSiegfried M. Rump. jcam, 372:112610, 2020. [doi]

2019

Sharp estimates for perturbation errors in summationsMarko Lange, Siegfried M. Rump. moc, 88(315):349-368, 2019. [doi]

Error Bounds for Computer ArithmeticsSiegfried M. Rump. arith 2019: 1-14 [doi]

2018

Piecewise smooth system and optimization with piecewise linearization via algorithmic differentiation (NII Shonan Meeting 2018-9)Andreas Griewank, Andrea Walther, Koichi Kubota, Siegfried M. Rump. shonan-reports, 2018, 2018. [doi]

On relative errors of floating-point operations: Optimal bounds and applicationsClaude-Pierre Jeannerod, Siegfried M. Rump. moc, 87(310):803-819, 2018. [doi]

Mathematically rigorous global optimization in floating-point arithmeticSiegfried M. Rump. oms, 33(4-6):771-798, 2018. [doi]

2017

mSiegfried M. Rump. TOMS, 43(3), 2017. [doi]

2015

The Componentwise Structured and Unstructured Backward Errors Can be Arbitrarily Far ApartSiegfried M. Rump. siammax, 36(2):385-392, 2015. [doi]

2014

Verified Bounds for the p-Norm Condition NumberSiegfried M. Rump. rc, 20:45-52, 2014. [doi]

Improved Backward Error Bounds for LU and Cholesky FactorizationsSiegfried M. Rump, Claude-Pierre Jeannerod. siammax, 35(2):684-698, 2014. [doi]

Improved componentwise verified error bounds for least squares problems and underdetermined linear systemsSiegfried M. Rump. na, 66(2):309-322, 2014. [doi]

2013

Improved Error Bounds for Inner Products in Floating-Point ArithmeticClaude-Pierre Jeannerod, Siegfried M. Rump. siammax, 34(2):338-344, 2013. [doi]

A consideration on the condition number of extremely ill-conditioned matricesTetsuo Nishi, Siegfried M. Rump, Shin'ichi Oishi. ecctd 2013: 1-4 [doi]

Accurate solution of dense linear systems, part I: Algorithms in rounding to nearestSiegfried M. Rump. jcam, 242:157-184, 2013. [doi]

Accurate solution of dense linear systems, Part II: Algorithms using directed roundingSiegfried M. Rump. jcam, 242:185-212, 2013. [doi]

2012

2010

2009

09471 Executive Summary - Computer-assisted proofs - tools, methods and applicationsB. Malcolm Brown, Erich Kaltofen, Shin'ichi Oishi, Siegfried M. Rump. Dagstuhl 2009: [doi]

09471 Abstracts Collection - Computer-assisted proofs - tools, methods and applicationsB. Malcolm Brown, Erich Kaltofen, Shin'ichi Oishi, Siegfried M. Rump. Dagstuhl 2009: [doi]

Ultimately Fast Accurate SummationSiegfried M. Rump. siamsc, 31(5):3466-3502, 2009. [doi]

2008

Accurate Floating-Point Summation Part II: Sign, K-Fold Faithful and Rounding to NearestSiegfried M. Rump, Takeshi Ogita, Shin ichi Oishi. siamsc, 31(2):1269-1302, 2008. [doi]

Accurate Floating-Point Summation Part I: Faithful RoundingSiegfried M. Rump, Takeshi Ogita, Shin ichi Oishi. siamsc, 31(1):189-224, 2008. [doi]

A parallel algorithm for accurate dot productN. Yamanaka, Takeshi Ogita, Siegfried M. Rump, Shin ichi Oishi. pc, 34(6-8):392-410, 2008. [doi]

2006

Towards Optimal Use of Multi-Precision Arithmetic: A RemarkVladik Kreinovich, Siegfried M. Rump. rc, 12(5):365-369, 2006. [doi]

2005

05391 Executive Summary - Numerical and Algebraic Algorithms and Computer-assisted ProofsBruno Buchberger, Christian Jansson, Shin ichi Oishi, Michael Plum, Siegfried M. Rump. Dagstuhl 2006: [doi]

05391 Abstracts Collection - Algebraic and Numerical Algorithms and Computer-assisted ProofsBruno Buchberger, Shin ichi Oishi, Michael Plum, Siegfried M. Rump. Dagstuhl 2006: [doi]

Accurate Sum and Dot ProductTakeshi Ogita, Siegfried M. Rump, Shin ichi Oishi. siamsc, 26(6):1955-1988, 2005. [doi]

10. Computer-Assisted Proofs and Self-Validating MethodsSiegfried M. Rump. In Bo Einarsson, editor, Accuracy and Reliability in Scientific Computing. Volume 18 of Software, Environments, Tools, pages 195-240, SIAM, 2005. [doi]

2003

On Nishi's Conditions for Ω-PropertySiegfried M. Rump. ieiceta, 86-A(9):2357-2359, 2003. [doi]

Structured Perturbations Part I: Normwise DistancesSiegfried M. Rump. siammax, 25(1):1-30, 2003. [doi]

Structured Perturbations Part II: Componentwise DistancesSiegfried M. Rump. siammax, 25(1):31-56, 2003. [doi]

2002

Fast verification of solutions of matrix equationsShin'ichi Oishi, Siegfried M. Rump. nm, 90(4):755-773, 2002. [doi]

2001

Introduction: Symbolic Algebraic Methods and Verification MethodsGötz Alefeld, Jiri Rohn, Siegfried M. Rump, Tetsuro Yamamoto. In Götz Alefeld, Jiri Rohn, Siegfried M. Rump, Tetsuro Yamamoto, editors, Symbolic Algebraic Methods and Verification Methods. pages 1-2, Springer, 2001.

Fast Verification Algorithms in MATLABSiegfried M. Rump. In Götz Alefeld, Jiri Rohn, Siegfried M. Rump, Tetsuro Yamamoto, editors, Symbolic Algebraic Methods and Verification Methods. pages 209-226, Springer, 2001.

Conservatism of the circle criterion-solution of a problem posed by A. MegretskiSiegfried M. Rump. tac, 46(10):1605-1608, 2001. [doi]

1999

Ill-Conditioned Matrices Are Componentwise Near to SingularitySiegfried M. Rump. siamrev, 41(1):102-112, 1999. [doi]

1998

Intervals and the Origins of CalculusDavid Dennis, Vladik Kreinovich, Siegfried M. Rump. rc, 4(2):191-197, 1998. [doi]

A Note on Epsilon-InflationSiegfried M. Rump. rc, 4(4):371-375, 1998. [doi]

INTLAB - INTerval LABoratorySiegfried M. Rump. scan 1999: 77-104 [doi]

1997

Inclusion of Zeros of Nowhere Differentiable n-Dimensional FunctionsSiegfried M. Rump. rc, 3(1):5-16, 1997. [doi]

Bounds for the Componentwise Distance to the Nearest Singular MatrixSiegfried M. Rump. siammax, 18(1):83-103, January 1997. [doi]

1996

Improved Iteration Schemes for Validation Algorithms for DenseSparse Nonlinear SystemsSiegfried M. Rump. computing, 57(1):77-84, 1996. [doi]

Expansion and estimation of the range of nonlinear functionsSiegfried M. Rump. moc, 65(216):1503-1512, 1996.

1995

Inclusion methods for real and complex functions in one variableDalcidio Moraes Claudio, Siegfried M. Rump. rita, 2(1):125-136, 1995.

1992

On the solution of interval linear systemsSiegfried M. Rump. computing, 47(3-4):337-353, 1992. [doi]

1991

Rigorous solution of linear programming problems with uncertain dataChristian Jansson, Siegfried M. Rump. mmor, 35(2):87-111, 1991. [doi]

Accuracy Control and Estimation, Self-Validating Systems and Software Environments for Scientific ComputationSiegfried M. Rump. ifip2-5 1992: 49-56

1989

Guaranteed inclusions for the complex generalized eigenproblemSiegfried M. Rump. computing, 42(2-3):225-238, 1989. [doi]

1987

FORTRAN-SC a study of a FORTRAN extension for engineering/scientific computation with access to ACRITHJ. Hartmut Bleher, Siegfried M. Rump, Ulrich W. Kulisch, M. Metzger, Christian P. Ullrich, W. Walter. computing, 39(2):93-110, 1987. [doi]

Algebraic Computation, Numerical Computation and Verified InclusionsSiegfried M. Rump. ibm 1988: 177-197

1986

Sichere Ergebnisse auf RechenanlagenSiegfried M. Rump. insk, 9(3):174-183, 1986.

1985

1983

Least significant bit evaluation of arithmetic expressions in single-precisionSiegfried M. Rump, Harald Böhm. computing, 30(3):189-199, 1983. [doi]

Mathematik auf dem RechnerSiegfried M. Rump. it, 25(6):126-132, 1983.

1982

1980

Generalized iteration methods for bounds of the solution of fixed point operator-equationsEdgar Kaucher, Siegfried M. Rump. computing, 24(2-3):131-137, 1980. [doi]

Zur Rückführung nicht mehr benötigten Speicherplatzes in PASCALSiegfried M. Rump. it, 22(2):55-62, 1980.

Notiz zur Genauigkeit der Arithmetik in RechenanlagenSiegfried M. Rump. it, 22(5):243-244, 1980.

1977

Real root isolation for algebraic polynomialsSiegfried M. Rump. cca, 11(2):2-3, 1977. [doi]

1976

On the sign of a real algebraic numberSiegfried M. Rump. issac 1976: 238-241 [doi]

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