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 56 Citations 20,256 205 World Ranking 356 National Ranking 192

Research.com Recognitions

Awards & Achievements

2013 - Fellow of the American Mathematical Society

2012 - SIAM Fellow For contributions to matrix analysis, numerical analysis, complex variables, and approximation theory.

1962 - Fellow of John Simon Guggenheim Memorial Foundation

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Algebra
  • Real number

Richard S. Varga mainly investigates Applied mathematics, Mathematical analysis, Numerical analysis, Discrete mathematics and Pure mathematics. The concepts of his Applied mathematics study are interwoven with issues in Matrix, Alternating direction implicit method, Spline interpolation, Thin plate spline and Iterative method. He brings together Matrix and Iterative analysis to produce work in his papers.

Mathematical analysis is closely attributed to Successive over-relaxation in his work. His Numerical analysis research integrates issues from Nonlinear boundary value problem, Mathematical optimization and Approximation theory. His Pure mathematics study incorporates themes from Eigenvalues and eigenvectors, Diagonally dominant matrix and Combinatorics.

His most cited work include:

  • Matrix iterative analysis (4725 citations)
  • Matrix Iterative Analysis (727 citations)
  • Proof of Theorem 2 (539 citations)

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

Richard S. Varga mainly focuses on Mathematical analysis, Combinatorics, Applied mathematics, Discrete mathematics and Pure mathematics. His study in Numerical analysis, Complex plane, Boundary value problem, Chebyshev iteration and Analytic function are all subfields of Mathematical analysis. The concepts of his Combinatorics study are interwoven with issues in Upper and lower bounds, Polynomial, Invertible matrix and Diagonally dominant matrix.

His studies deal with areas such as Iterative method, Mathematical optimization and Interpolation as well as Applied mathematics. His work is dedicated to discovering how Iterative method, Matrix are connected with Eigenvalues and eigenvectors and other disciplines. Throughout his Discrete mathematics studies, Richard S. Varga incorporates elements of other sciences such as Proof of impossibility and Original proof of Gödel's completeness theorem.

He most often published in these fields:

  • Mathematical analysis (26.24%)
  • Combinatorics (24.33%)
  • Applied mathematics (21.29%)

What were the highlights of his more recent work (between 1994-2012)?

  • Combinatorics (24.33%)
  • Mathematical analysis (26.24%)
  • Matrix (12.55%)

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

His primary scientific interests are in Combinatorics, Mathematical analysis, Matrix, Applied mathematics and Iterative method. His Combinatorics research is multidisciplinary, incorporating elements of Invertible matrix, Singular value decomposition, Inverse, Ultrametric space and Potential theory. Richard S. Varga interconnects Motion and Discrepancy theory in the investigation of issues within Mathematical analysis.

His research in the fields of Diagonally dominant matrix overlaps with other disciplines such as Block. He conducts interdisciplinary study in the fields of Applied mathematics and Iterative analysis through his research. Richard S. Varga combines subjects such as Chebyshev filter, Order, Acceleration and System of linear equations with his study of Iterative method.

Between 1994 and 2012, his most popular works were:

  • Matrix Iterative Analysis (727 citations)
  • Geršgorin and his circles (299 citations)
  • Encyclopaedia of Mathematics, Supplement III (52 citations)

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

  • Mathematical analysis
  • Algebra
  • Real number

His scientific interests lie mostly in Pure mathematics, Matrix, Combinatorics, Numerical analysis and Type. His Pure mathematics research incorporates themes from Sine and Algebra. His Matrix study incorporates themes from Invertible matrix, Inverse and Applied mathematics.

The Combinatorics study combines topics in areas such as Zero, Sequence, Mathematical analysis and Domain. His studies examine the connections between Type and genetics, as well as such issues in Eigenvalues and eigenvectors, with regards to Lemniscate, Artificial intelligence and Linear algebra. In his research on the topic of Diagonally dominant matrix, Discrete mathematics is strongly related with Matrix pencil.

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

Matrix iterative analysis

Richard S. Varga.
(1961)

6970 Citations

Matrix Iterative Analysis

Steve Abbott;Richard S. Varga.
The Mathematical Gazette (2000)

1138 Citations

Proof of Theorem 2

Albert Edrei;Edward B. Saff;Richard S. Varga.
(1983)

869 Citations

Proof of Theorem 4

Albert Edrei;Edward B. Saff;Richard S. Varga.
(1983)

716 Citations

Geršgorin and his circles

Richard S. Varga.
(2004)

457 Citations

Proof of Theorem 5

Albert Edrei;Edward B. Saff;Richard S. Varga.
(1983)

448 Citations

Block diagonally dominant matrices and generalizations of the Gerschgorin circle theorem

David G. Feingold;Richard S. Varga.
Pacific Journal of Mathematics (1962)

422 Citations

Numerical methods of high-order accuracy for nonlinear boundary value problems

P. G. Ciarlet;M. H. Schultz;R. S. Varga.
Numerische Mathematik (1968)

390 Citations

Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods

Gene H. Golub;Richard S. Varga.
Numerische Mathematik (1961)

376 Citations

Piecewise Hermite interpolation in one and two variables with applications to partial differential equations

G. Birkhoff;M. H. Schultz;R. S. Varga.
Numerische Mathematik (1968)

305 Citations

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