On the sign of a real algebraic number. - Siegfried M. Rump (SYMSACC, 1976)

Real root isolation for algebraic polynomials. - Siegfried M. Rump (SIGSAM Bull., 1977)

Generalized iteration methods for bounds of the solution of fixed point operator-equations. - Edgar Kaucher; Siegfried M. Rump (Computing, 1980)

Zur Rückführung nicht mehr benötigten Speicherplatzes in PASCAL. - Siegfried M. Rump (Elektron. Rechenanlagen, 1980)

Notiz zur Genauigkeit der Arithmetik in Rechenanlagen. - Siegfried M. Rump (Elektron. Rechenanlagen, 1980)

Rechnervorführung, Pakete für Standardprobleme der Numerik. - Siegfried M. Rump (Wissenschaftliches Rechnen und Programmiersprachen, 1982)

Lösung linearer und nichtlinearer Gleichungssysteme mit maximaler Genauigkeit. - Siegfried M. Rump (Wissenschaftliches Rechnen und Programmiersprachen, 1982)

Solving Algebraic Problems with High Accuracy. - Siegfried M. Rump (IMACS World Congress, 1982)

E-methods for fixed point equations f(x)=x. - Edgar Kaucher; Siegfried M. Rump (Computing, 1982)

Solving nonlinear systems with least significant bit accuracy. - Siegfried M. Rump (Computing, 1982)

Computer und Rechengenauigkeit. - Siegfried M. Rump (Elektron. Rechenanlagen, 1982)

Least significant bit evaluation of arithmetic expressions in single-precision. - Siegfried M. Rump; Harald Böhm (Computing, 1983)

Mathematik auf dem Rechner. - Siegfried M. Rump (Elektron. Rechenanlagen, 1983)

Case Studies for Augmented Floating-Point. - Willard L. Miranker; Michael Mascagni; Siegfried M. Rump (Accurate Scientific Computations, 1985)

New Results on Verified Inclusions. - Siegfried M. Rump (Accurate Scientific Computations, 1985)

ACRITH: High-Accuracy Arithmetic an advanced tool for numerical computation. - J. Hartmut Bleher; A. E. Roeder; Siegfried M. Rump (IEEE Symposium on Computer Arithmetic, 1985)

Higher Order Computer Arithmetic. - Siegfried M. Rump (IEEE Symposium on Computer Arithmetic, 1985)

Numerical Methods with Automatic Verification. - Siegfried M. Rump (European Conference on Computer Algebra (2), 1985)

ACRITH - High Accuracy Arithmetic Subroutine Library. - Siegfried M. Rump (European Conference on Computer Algebra (2), 1985)

Sichere Ergebnisse auf Rechenanlagen. - Siegfried M. Rump (Inform. Spektrum, 1986)

Algebraic Computation, Numerical Computation and Verified Inclusions. - Siegfried M. Rump (Trends in Computer Algebra, 1987)

FORTRAN-SC a study of a FORTRAN extension for engineering/scientific computation with access to ACRITH. - J. Hartmut Bleher; Siegfried M. Rump; Ulrich W. Kulisch; M. Metzger; Christian P. Ullrich; W. Walter (Computing, 1987)

Guaranteed inclusions for the complex generalized eigenproblem. - Siegfried M. Rump (Computing, 1989)

Accuracy Control and Estimation, Self-Validating Systems and Software Environments for Scientific Computation. - Siegfried M. Rump (Programming Environments for High-Level Scientific Problem Solving, 1991)

Rigorous solution of linear programming problems with uncertain data. - Christian Jansson; Siegfried M. Rump (ZOR Methods Model. Oper. Res., 1991)

On the solution of interval linear systems. - Siegfried M. Rump (Computing, 1992)

Inclusion methods for real and complex functions in one variable. - Dalcidio Moraes Claudio; Siegfried M. Rump (RITA, 1995)

Improved Iteration Schemes for Validation Algorithms for DenseSparse Nonlinear Systems. - Siegfried M. Rump (Computing, 1996)

Expansion and estimation of the range of nonlinear functions. - Siegfried M. Rump (Math. Comput., 1996)

Inclusion of Zeros of Nowhere Differentiable n-Dimensional Functions. - Siegfried M. Rump (Reliab. Comput., 1997)

Bounds for the Componentwise Distance to the Nearest Singular Matrix. - Siegfried M. Rump (SIAM J. Matrix Anal. Appl., 1997)

INTLAB - INTerval LABoratory. - Siegfried M. Rump (SCAN, 1998)

Intervals and the Origins of Calculus. - David Dennis; Vladik Kreinovich; Siegfried M. Rump (Reliab. Comput., 1998)

A Note on Epsilon-Inflation. - Siegfried M. Rump (Reliab. Comput., 1998)

Ill-Conditioned Matrices Are Componentwise Near to Singularity. - Siegfried M. Rump (SIAM Rev., 1999)

Introduction: Symbolic Algebraic Methods and Verification Methods. - Götz Alefeld; Jiri Rohn; Siegfried M. Rump; Tetsuro Yamamoto (Symbolic Algebraic Methods and Verification Methods, 2001)

Fast Verification Algorithms in MATLAB. - Siegfried M. Rump (Symbolic Algebraic Methods and Verification Methods, 2001)

Conservatism of the circle criterion-solution of a problem posed by A. Megretski. - Siegfried M. Rump (IEEE Trans. Autom. Control., 2001)

Fast verification of solutions of matrix equations. - Shin'ichi Oishi; Siegfried M. Rump (Numerische Mathematik, 2002)

On Nishi's Conditions for Ω-Property. - Siegfried M. Rump (IEICE Trans. Fundam. Electron. Commun. Comput. Sci., 2003)

Structured Perturbations Part I: Normwise Distances. - Siegfried M. Rump (SIAM J. Matrix Anal. Appl., 2003)

Structured Perturbations Part II: Componentwise Distances. - Siegfried M. Rump (SIAM J. Matrix Anal. Appl., 2003)

10. Computer-Assisted Proofs and Self-Validating Methods. - Siegfried M. Rump (Accuracy and Reliability in Scientific Computing, 2005)

05391 Executive Summary - Numerical and Algebraic Algorithms and Computer-assisted Proofs. - Bruno Buchberger; Christian Jansson; Shin'ichi Oishi; Michael Plum; Siegfried M. Rump (Algebraic and Numerical Algorithms and Computer-assisted Proofs, 2005)

05391 Abstracts Collection - Algebraic and Numerical Algorithms and Computer-assisted Proofs. - Bruno Buchberger; Shin'ichi Oishi; Michael Plum; Siegfried M. Rump (Algebraic and Numerical Algorithms and Computer-assisted Proofs, 2005)

Accurate Sum and Dot Product. - Takeshi Ogita; Siegfried M. Rump; Shin'ichi Oishi (SIAM J. Sci. Comput., 2005)

Towards Optimal Use of Multi-Precision Arithmetic: A Remark. - Vladik Kreinovich; Siegfried M. Rump (Reliab. Comput., 2006)

A parallel algorithm for accurate dot product. - Naoya Yamanaka; Takeshi Ogita; Siegfried M. Rump; Shin'ichi Oishi (Parallel Comput., 2008)

Accurate Floating-Point Summation Part I: Faithful Rounding. - Siegfried M. Rump; Takeshi Ogita; Shin'ichi Oishi (SIAM J. Sci. Comput., 2008)

Accurate Floating-Point Summation Part II: Sign, K-Fold Faithful and Rounding to Nearest. - Siegfried M. Rump; Takeshi Ogita; Shin'ichi Oishi (SIAM J. Sci. Comput., 2008)

09471 Abstracts Collection - Computer-assisted proofs - tools, methods and applications. - B. Malcolm Brown; Erich L. Kaltofen; Shin'ichi Oishi; Siegfried M. Rump (Computer-assisted proofs - tools, methods and applications, 2009)

09471 Executive Summary - Computer-assisted proofs - tools, methods and applications. - B. Malcolm Brown; Erich L. Kaltofen; Shin'ichi Oishi; Siegfried M. Rump (Computer-assisted proofs - tools, methods and applications, 2009)

Ultimately Fast Accurate Summation. - Siegfried M. Rump (SIAM J. Sci. Comput., 2009)

Accurate and Reliable Computing in Floating-Point Arithmetic. - Siegfried M. Rump (ICMS, 2010)

Verification methods: Rigorous results using floating-point arithmetic. - Siegfried M. Rump (Acta Numer., 2010)

Verified error bounds for multiple roots of systems of nonlinear equations. - Siegfried M. Rump; Stef Graillat (Numer. Algorithms, 2010)

Fast Verification for All Eigenpairs in Symmetric Positive Definite Generalized Eigenvalue Problems. - Shinya Miyajima; Takeshi Ogita; Siegfried M. Rump; Shin'ichi Oishi (Reliab. Comput., 2010)

Fast algorithms for floating-point interval matrix multiplication. - Katsuhisa Ozaki; Takeshi Ogita; Siegfried M. Rump; Shin'ichi Oishi (J. Comput. Appl. Math., 2012)

Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications. - Katsuhisa Ozaki; Takeshi Ogita; Shin'ichi Oishi; Siegfried M. Rump (Numer. Algorithms, 2012)

Fast interval matrix multiplication. - Siegfried M. Rump (Numer. Algorithms, 2012)

Verified Bounds for Least Squares Problems and Underdetermined Linear Systems. - Siegfried M. Rump (SIAM J. Matrix Anal. Appl., 2012)

A consideration on the condition number of extremely ill-conditioned matrices. - Tetsuo Nishi; Siegfried M. Rump; Shin'ichi Oishi (ECCTD, 2013)

Accurate solution of dense linear systems, part I: Algorithms in rounding to nearest. - Siegfried M. Rump (J. Comput. Appl. Math., 2013)

Accurate solution of dense linear systems, Part II: Algorithms using directed rounding. - Siegfried M. Rump (J. Comput. Appl. Math., 2013)

Improved Error Bounds for Inner Products in Floating-Point Arithmetic. - Claude-Pierre Jeannerod; Siegfried M. Rump (SIAM J. Matrix Anal. Appl., 2013)

Improved componentwise verified error bounds for least squares problems and underdetermined linear systems. - Siegfried M. Rump (Numer. Algorithms, 2014)

Verified Bounds for the p-Norm Condition Number. - Siegfried M. Rump (Reliab. Comput., 2014)

Improved Backward Error Bounds for LU and Cholesky Factorizations. - Siegfried M. Rump; Claude-Pierre Jeannerod (SIAM J. Matrix Anal. Appl., 2014)

The Componentwise Structured and Unstructured Backward Errors Can be Arbitrarily Far Apart. - Siegfried M. Rump (SIAM J. Matrix Anal. Appl., 2015)

IEEE754 Precision-k base-β Arithmetic Inherited by Precision-m Base-β Arithmetic for k < m. - Siegfried M. Rump (ACM Trans. Math. Softw., 2017)

On relative errors of floating-point operations: Optimal bounds and applications. - Claude-Pierre Jeannerod; Siegfried M. Rump (Math. Comput., 2018)

Mathematically rigorous global optimization in floating-point arithmetic. - Siegfried M. Rump (Optim. Methods Softw., 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 (NII Shonan Meet. Rep., 2018)

Error Bounds for Computer Arithmetics. - Siegfried M. Rump (ARITH, 2019)

Sharp estimates for perturbation errors in summations. - Marko Lange; Siegfried M. Rump (Math. Comput., 2019)

Modified error bounds for approximate solutions of dense linear systems. - Atsushi Minamihata; Takeshi Ogita; Siegfried M. Rump; Shin'ichi Oishi (J. Comput. Appl. Math., 2020)

Verified bounds for the determinant of real or complex point or interval matrices. - Siegfried M. Rump (J. Comput. Appl. Math., 2020)

Faithfully Rounded Floating-point Computations. - Marko Lange; Siegfried M. Rump (ACM Trans. Math. Softw., 2020)

Foreword. - Mitsuhiro T. Nakao; Takeshi Ogita; Siegfried M. Rump (J. Comput. Appl. Math., 2021)

Convergence results for some piecewise linear solvers. - Manuel Radons; Siegfried M. Rump (Optim. Lett., 2022)

Verified Error Bounds for All Eigenvalues and Eigenvectors of a Matrix. - Siegfried M. Rump (SIAM J. Matrix Anal. Appl., 2022)

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. - Siegfried M. Rump; Marko Lange (J. Comput. Appl. Math., 2023)

IEEE-754 Precision-p base-β Arithmetic Implemented in Binary. - Siegfried M. Rump (ACM Trans. Math. Softw., 2023)

Verified Error Bounds for Matrix Decompositions. - Siegfried M. Rump; Takeshi Ogita (SIAM J. Matrix Anal. Appl., 2024)