D-Index & Metrics Best Publications

D-Index & Metrics

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 30 Citations 5,129 144 World Ranking 2137 National Ranking 138

Overview

What is he best known for?

The fields of study he is best known for:

  • Algebra
  • Complex number
  • Mathematical analysis

Siegfried M. Rump mostly deals with Algorithm, Rounding, Floating point, Round-off error and Condition number. His Algorithm research incorporates themes from Complex number, Multiplication, Numerical analysis and Interval. His Rounding study incorporates themes from Cholesky decomposition, Hermitian matrix and Combinatorics.

The various areas that he examines in his Floating point study include Arbitrary-precision arithmetic and Arithmetic. His Arbitrary-precision arithmetic research integrates issues from Arithmetic function, Sparse matrix and MATLAB. His Condition number research is multidisciplinary, relying on both Circulant matrix, Linear system and Toeplitz matrix, Pure mathematics.

His most cited work include:

  • INTLAB — INTerval LABoratory (873 citations)
  • Accurate Sum and Dot Product (307 citations)
  • Verification methods: Rigorous results using floating-point arithmetic (185 citations)

What are the main themes of his work throughout his whole career to date?

His primary areas of investigation include Algorithm, Floating point, Rounding, Linear system and Matrix. His work deals with themes such as Interval arithmetic, Interval, Numerical analysis and Dot product, which intersect with Algorithm. His study looks at the relationship between Floating point and fields such as Arithmetic, as well as how they intersect with chemical problems.

His Rounding study combines topics in areas such as Arithmetic underflow, Round-off error, Machine epsilon, Simple and IEEE floating point. His Linear system study combines topics from a wide range of disciplines, such as Correctness, H matrix, Mathematical optimization, Toeplitz matrix and Applied mathematics. His Matrix research includes elements of Discrete mathematics, Bounded function and Combinatorics.

He most often published in these fields:

  • Algorithm (32.48%)
  • Floating point (23.93%)
  • Rounding (28.21%)

What were the highlights of his more recent work (between 2016-2021)?

  • Combinatorics (21.37%)
  • Matrix (22.22%)
  • Real number (5.98%)

In recent papers he was focusing on the following fields of study:

His scientific interests lie mostly in Combinatorics, Matrix, Real number, Applied mathematics and Floating point. His work on Disjoint sets as part of his general Combinatorics study is frequently connected to Perturbation, thereby bridging the divide between different branches of science. His Matrix research is multidisciplinary, incorporating elements of Piecewise linear function, Eigenvalues and eigenvectors, Product and Absolute value equation.

His studies in Real number integrate themes in fields like Well-defined, Recursion, Arithmetic, Rounding and Extended precision. His work carried out in the field of Rounding brings together such families of science as Fixed point and Limit. His work in Floating point tackles topics such as Round-off error which are related to areas like Discrete mathematics, Square root and Base.

Between 2016 and 2021, his most popular works were:

  • On relative errors of floating-point operations: Optimal bounds and applications (17 citations)
  • Sharp estimates for perturbation errors in summations (6 citations)
  • Bounds for the determinant by Gershgorin circles (3 citations)

In his most recent research, the most cited papers focused on:

  • Algebra
  • Complex number
  • Real number

Siegfried M. Rump mainly investigates Combinatorics, Floating point, Real number, Round-off error and Matrix. His studies examine the connections between Combinatorics and genetics, as well as such issues in Diagonal, with regards to Identity matrix, Upper and lower bounds, Matrix norm and Toeplitz matrix. His Real number study frequently links to other fields, such as Rounding.

The study incorporates disciplines such as Standard algorithms, Matrix multiplication, Cholesky decomposition and Arithmetic in addition to Rounding. His work is dedicated to discovering how Round-off error, Square root are connected with Unit, Arithmetic underflow, Function, Base and Expression and other disciplines. His Matrix research incorporates elements of Disjoint sets, Eigenvalues and eigenvectors and Product.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

INTLAB — INTerval LABoratory

Siegfried M. Rump.
Developments in Reliable Computing (1999)

1399 Citations

Accurate Sum and Dot Product

Takeshi Ogita;Siegfried M. Rump;Shin'ichi Oishi.
SIAM Journal on Scientific Computing (2005)

466 Citations

Verification methods: Rigorous results using floating-point arithmetic

Siegfried M. Rump.
Acta Numerica (2010)

277 Citations

Verification methods for dense and sparse systems of equations

Siegfried M. Rump.
(1994)

272 Citations

Solving algebraic problems with high accuracy

Siegfried M. Rump.
Proc. of the symposium on A new approach to scientific computation (1983)

258 Citations

Accurate Floating-Point Summation Part I: Faithful Rounding

Siegfried M. Rump;Takeshi Ogita;Shin'ichi Oishi.
SIAM Journal on Scientific Computing (2008)

201 Citations

Fast and Parallel Interval Arithmetic

Siegfried M. Rump.
Bit Numerical Mathematics (1999)

194 Citations

Kleine Fehlerschranken bei Matrixproblemen

Siegfried M. Rump.
(1980)

129 Citations

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

Siegfried M. Rump;Takeshi Ogita;Shin'ichi Oishi.
SIAM Journal on Scientific Computing (2008)

104 Citations

On the solution of interval linear systems

S. M. Rump.
Computing (1991)

91 Citations

Best Scientists Citing Siegfried M. Rump

Victor Y. Pan

Victor Y. Pan

City University of New York

Publications: 22

Arnold Neumaier

Arnold Neumaier

University of Vienna

Publications: 22

Yimin Wei

Yimin Wei

Fudan University

Publications: 17

Vladik Kreinovich

Vladik Kreinovich

The University of Texas at El Paso

Publications: 15

Andreas Frommer

Andreas Frommer

University of Wuppertal

Publications: 11

James Demmel

James Demmel

University of California, Berkeley

Publications: 11

Xiaojun Chen

Xiaojun Chen

Hong Kong Polytechnic University

Publications: 10

Enrique S. Quintana-Ortí

Enrique S. Quintana-Ortí

Universitat Politècnica de València

Publications: 8

Hao Zhang

Hao Zhang

University of Sydney

Publications: 8

Anil V. Rao

Anil V. Rao

University of Florida

Publications: 8

Erich Kaltofen

Erich Kaltofen

North Carolina State University

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Andreas Griewank

Andreas Griewank

Humboldt-Universität zu Berlin

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Eric Feron

Eric Feron

King Abdullah University of Science and Technology

Publications: 6

Matthias Althoff

Matthias Althoff

Technical University of Munich

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Bernard Mourrain

Bernard Mourrain

French Institute for Research in Computer Science and Automation - INRIA

Publications: 6

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking d-index is inferred from publications deemed to belong to the considered discipline.

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