Siegfried M. Rump

ACM Trans. Math. Softw., December, 2023

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.

[BibT_eX]

[DOI]

Marko Lange

J. Comput. Appl. Math., December, 2023

2022

Verified Error Bounds for All Eigenvalues and Eigenvectors of a Matrix.

[BibT_eX]

[DOI]

SIAM J. Matrix Anal. Appl., 2022

Convergence results for some piecewise linear solvers.

[BibT_eX]

[DOI]

Manuel Radons

Optim. Lett., 2022

2021

Foreword.

[BibT_eX]

[DOI]

Mitsuhiro T. Nakao

J. Comput. Appl. Math., 2021

2020

Faithfully Rounded Floating-point Computations.

[BibT_eX]

[DOI]

Marko Lange

ACM Trans. Math. Softw., 2020

Verified bounds for the determinant of real or complex point or interval matrices.

[BibT_eX]

[DOI]

J. Comput. Appl. Math., 2020

Modified error bounds for approximate solutions of dense linear systems.

[BibT_eX]

[DOI]

J. Comput. Appl. Math., 2020

2019

Sharp estimates for perturbation errors in summations.

[BibT_eX]

[DOI]

Marko Lange

Math. Comput., 2019

Error Bounds for Computer Arithmetics.

[BibT_eX]

[DOI]

Proceedings of the 26th IEEE Symposium on Computer Arithmetic, 2019

2018

Piecewise smooth system and optimization with piecewise linearization via algorithmic differentiation (NII Shonan Meeting 2018-9).

[BibT_eX]

[DOI]

NII Shonan Meet. Rep., 2018

Mathematically rigorous global optimization in floating-point arithmetic.

[BibT_eX]

[DOI]

Optim. Methods Softw., 2018

On relative errors of floating-point operations: Optimal bounds and applications.

[BibT_eX]

[DOI]

Claude-Pierre Jeannerod

Math. Comput., 2018

2017

IEEE754 Precision-k base-β Arithmetic Inherited by Precision-m Base-β Arithmetic for k < m.

[BibT_eX]

[DOI]

ACM Trans. Math. Softw., 2017

2015

The Componentwise Structured and Unstructured Backward Errors Can be Arbitrarily Far Apart.

[BibT_eX]

[DOI]

SIAM J. Matrix Anal. Appl., 2015

2014

Improved Backward Error Bounds for LU and Cholesky Factorizations.

[BibT_eX]

[DOI]

Claude-Pierre Jeannerod

SIAM J. Matrix Anal. Appl., 2014

Verified Bounds for the p-Norm Condition Number.

[BibT_eX]

[DOI]

Reliab. Comput., 2014

Improved componentwise verified error bounds for least squares problems and underdetermined linear systems.

[BibT_eX]

[DOI]

Numer. Algorithms, 2014

2013

Improved Error Bounds for Inner Products in Floating-Point Arithmetic.

[BibT_eX]

[DOI]

Claude-Pierre Jeannerod

SIAM J. Matrix Anal. Appl., 2013

Accurate solution of dense linear systems, Part II: Algorithms using directed rounding.

[BibT_eX]

[DOI]

J. Comput. Appl. Math., 2013

Accurate solution of dense linear systems, part I: Algorithms in rounding to nearest.

[BibT_eX]

[DOI]

J. Comput. Appl. Math., 2013

A consideration on the condition number of extremely ill-conditioned matrices.

[BibT_eX]

[DOI]

Tetsuo Nishi

Proceedings of the 21st European Conference on Circuit Theory and Design, 2013

2012

Verified Bounds for Least Squares Problems and Underdetermined Linear Systems.

[BibT_eX]

[DOI]

SIAM J. Matrix Anal. Appl., 2012

Fast interval matrix multiplication.

[BibT_eX]

[DOI]

Numer. Algorithms, 2012

Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications.

[BibT_eX]

[DOI]

Numer. Algorithms, 2012

Fast algorithms for floating-point interval matrix multiplication.

[BibT_eX]

[DOI]

J. Comput. Appl. Math., 2012

2010

Fast Verification for All Eigenpairs in Symmetric Positive Definite Generalized Eigenvalue Problems.

[BibT_eX]

[DOI]

Reliab. Comput., 2010

Verified error bounds for multiple roots of systems of nonlinear equations.

[BibT_eX]

[DOI]

Stef Graillat

Numer. Algorithms, 2010

Verification methods: Rigorous results using floating-point arithmetic.

[BibT_eX]

[DOI]

Acta Numer., 2010

Accurate and Reliable Computing in Floating-Point Arithmetic.

[BibT_eX]

[DOI]

Proceedings of the Mathematical Software, 2010

2009

Ultimately Fast Accurate Summation.

[BibT_eX]

[DOI]

SIAM J. Sci. Comput., 2009

09471 Executive Summary - Computer-assisted proofs - tools, methods and applications.

[BibT_eX]

[DOI]

Proceedings of the Computer-assisted proofs - tools, methods and applications, 15.11., 2009

09471 Abstracts Collection - Computer-assisted proofs - tools, methods and applications.

[BibT_eX]

[DOI]

Proceedings of the Computer-assisted proofs - tools, methods and applications, 15.11., 2009

2008

Accurate Floating-Point Summation Part II: Sign, K-Fold Faithful and Rounding to Nearest.

[BibT_eX]

[DOI]

SIAM J. Sci. Comput., 2008

Accurate Floating-Point Summation Part I: Faithful Rounding.

[BibT_eX]

[DOI]

SIAM J. Sci. Comput., 2008

A parallel algorithm for accurate dot product.

[BibT_eX]

[DOI]

Parallel Comput., 2008

2006

Towards Optimal Use of Multi-Precision Arithmetic: A Remark.

[BibT_eX]

[DOI]

Vladik Kreinovich

Reliab. Comput., 2006

2005

Accurate Sum and Dot Product.

[BibT_eX]

[DOI]

SIAM J. Sci. Comput., 2005

05391 Abstracts Collection - Algebraic and Numerical Algorithms and Computer-assisted Proofs.

[BibT_eX]

[DOI]

Proceedings of the Algebraic and Numerical Algorithms and Computer-assisted Proofs, 2005

05391 Executive Summary - Numerical and Algebraic Algorithms and Computer-assisted Proofs.

[BibT_eX]

[DOI]

Proceedings of the Algebraic and Numerical Algorithms and Computer-assisted Proofs, 2005

10. Computer-Assisted Proofs and Self-Validating Methods.

[BibT_eX]

[DOI]

Proceedings of the Accuracy and Reliability in Scientific Computing, 2005

2003

Structured Perturbations Part II: Componentwise Distances.

[BibT_eX]

[DOI]

SIAM J. Matrix Anal. Appl., 2003

Structured Perturbations Part I: Normwise Distances.

[BibT_eX]

[DOI]

SIAM J. Matrix Anal. Appl., 2003

On Nishi's Conditions for Ω-Property.

[BibT_eX]

[DOI]

IEICE Trans. Fundam. Electron. Commun. Comput. Sci., 2003

2002

Fast verification of solutions of matrix equations.

[BibT_eX]

[DOI]

Numerische Mathematik, 2002

2001

Conservatism of the circle criterion-solution of a problem posed by A. Megretski.

[BibT_eX]

[DOI]

IEEE Trans. Autom. Control., 2001

Fast Verification Algorithms in MATLAB.

[BibT_eX]

[DOI]

Proceedings of the Symbolic Algebraic Methods and Verification Methods, 2001

Introduction: Symbolic Algebraic Methods and Verification Methods.

[BibT_eX]

[DOI]

Proceedings of the Symbolic Algebraic Methods and Verification Methods, 2001

1999

Ill-Conditioned Matrices Are Componentwise Near to Singularity.

[BibT_eX]

[DOI]

SIAM Rev., 1999

1998

A Note on Epsilon-Inflation.

[BibT_eX]

[DOI]

Reliab. Comput., 1998

Intervals and the Origins of Calculus.

[BibT_eX]

[DOI]

David Dennis

Vladik Kreinovich

Reliab. Comput., 1998

INTLAB - INTerval LABoratory.

[BibT_eX]

[DOI]

Proceedings of the Developments in Reliable Computing, 1998

1997

Bounds for the Componentwise Distance to the Nearest Singular Matrix.

[BibT_eX]

[DOI]

SIAM J. Matrix Anal. Appl., January, 1997

Inclusion of Zeros of Nowhere Differentiable n-Dimensional Functions.

[BibT_eX]

[DOI]

Reliab. Comput., 1997

1996

Expansion and estimation of the range of nonlinear functions.

[BibT_eX]

[DOI]

Math. Comput., 1996

Improved Iteration Schemes for Validation Algorithms for DenseSparse Nonlinear Systems.

[BibT_eX]

[DOI]

Computing, 1996

1995

Inclusion methods for real and complex functions in one variable.

[BibT_eX]

Dalcidio Moraes Claudio

RITA, 1995

1992

On the solution of interval linear systems.

[BibT_eX]

[DOI]

Computing, 1992

1991

Rigorous solution of linear programming problems with uncertain data.

[BibT_eX]

[DOI]

Christian Jansson

ZOR Methods Model. Oper. Res., 1991

Accuracy Control and Estimation, Self-Validating Systems and Software Environments for Scientific Computation.

[BibT_eX]

Proceedings of the Programming Environments for High-Level Scientific Problem Solving, 1991

1989

Guaranteed inclusions for the complex generalized eigenproblem.

[BibT_eX]

[DOI]

Computing, 1989

1987

FORTRAN-SC a study of a FORTRAN extension for engineering/scientific computation with access to ACRITH.

[BibT_eX]

[DOI]

Computing, 1987

Algebraic Computation, Numerical Computation and Verified Inclusions.

[BibT_eX]

[DOI]

Proceedings of the Trends in Computer Algebra, 1987

1986

Sichere Ergebnisse auf Rechenanlagen.

[BibT_eX]

Inform. Spektrum, 1986

1985

ACRITH - High Accuracy Arithmetic Subroutine Library.

[BibT_eX]

[DOI]

Proceedings of the EUROCAL '85, 1985

Numerical Methods with Automatic Verification.

[BibT_eX]

[DOI]

Proceedings of the EUROCAL '85, 1985

Higher Order Computer Arithmetic.

[BibT_eX]

[DOI]

Proceedings of the 7th IEEE Symposium on Computer Arithmetic, 1985

ACRITH: High-Accuracy Arithmetic an advanced tool for numerical computation.

[BibT_eX]

[DOI]

J. Hartmut Bleher

A. E. Roeder

Proceedings of the 7th IEEE Symposium on Computer Arithmetic, 1985

New Results on Verified Inclusions.

[BibT_eX]

[DOI]

Proceedings of the Accurate Scientific Computations, 1985

Case Studies for Augmented Floating-Point.

[BibT_eX]

[DOI]

Willard L. Miranker

Michael Mascagni

Proceedings of the Accurate Scientific Computations, 1985

1983

Mathematik auf dem Rechner.

[BibT_eX]

Elektron. Rechenanlagen, 1983

Least significant bit evaluation of arithmetic expressions in single-precision.

[BibT_eX]

[DOI]

Harald Böhm

Computing, 1983

1982

Computer und Rechengenauigkeit.

[BibT_eX]

[DOI]

Elektron. Rechenanlagen, 1982

Solving nonlinear systems with least significant bit accuracy.

[BibT_eX]

[DOI]

Computing, 1982

E-methods for fixed point equations f(x)=x.

[BibT_eX]

[DOI]

Edgar Kaucher

Computing, 1982

Solving Algebraic Problems with High Accuracy.

[BibT_eX]

Proceedings of the Parallel and Large-Scale Computers: Performance, 1982

Lösung linearer und nichtlinearer Gleichungssysteme mit maximaler Genauigkeit.

[BibT_eX]

Proceedings of the Wissenschaftliches Rechnen und Programmiersprachen, 1982

Rechnervorführung, Pakete für Standardprobleme der Numerik.

[BibT_eX]

Proceedings of the Wissenschaftliches Rechnen und Programmiersprachen, 1982

1980

Notiz zur Genauigkeit der Arithmetik in Rechenanlagen.

[BibT_eX]

[DOI]

Elektron. Rechenanlagen, 1980

Zur Rückführung nicht mehr benötigten Speicherplatzes in PASCAL.

[BibT_eX]

[DOI]

Elektron. Rechenanlagen, 1980

Generalized iteration methods for bounds of the solution of fixed point operator-equations.

[BibT_eX]

[DOI]

Edgar Kaucher

Computing, 1980

1977

Real root isolation for algebraic polynomials.

[BibT_eX]

[DOI]

SIGSAM Bull., 1977

1976

On the sign of a real algebraic number.

[BibT_eX]

[DOI]