H-Index & Metrics Top Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics H-index 102 Citations 66,636 279 World Ranking 13 National Ranking 9

Research.com Recognitions

Awards & Achievements

1993 - Member of the National Academy of Sciences

1987 - Fellow of John Simon Guggenheim Memorial Foundation

1980 - Fellow of the American Association for the Advancement of Science (AAAS)

Overview

What is he best known for?

The fields of study he is best known for:

  • Eigenvalues and eigenvectors
  • Statistics
  • Mathematical analysis

His main research concerns Applied mathematics, Matrix, Mathematical analysis, Iterative method and Eigenvalues and eigenvectors. His studies in Applied mathematics integrate themes in fields like Hessenberg matrix, Hermitian matrix, Mathematical optimization and Preconditioner. In his research on the topic of Hessenberg matrix, QR decomposition is strongly related with Matrix exponential.

His Matrix study improves the overall literature in Algebra. The Iterative method study combines topics in areas such as Saddle point, Discretization, Linear system and Conjugate gradient method. His research in Eigenvalues and eigenvectors focuses on subjects like Singular value decomposition, which are connected to Rank, Ordinary least squares and Subspace topology.

His most cited work include:

  • Matrix computations (31102 citations)
  • Matrix computations (3rd ed.) (6069 citations)
  • Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter (2852 citations)

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

Applied mathematics, Mathematical analysis, Eigenvalues and eigenvectors, Matrix and Combinatorics are his primary areas of study. Gene H. Golub combines subjects such as Lanczos algorithm, Lanczos resampling, Mathematical optimization, Numerical analysis and Least squares with his study of Applied mathematics. His Mathematical optimization research integrates issues from Estimation theory and Algorithm.

The concepts of his Mathematical analysis study are interwoven with issues in Positive-definite matrix, Iterative method, Conjugate gradient method and Rate of convergence. Gene H. Golub has included themes like Inverse and Symmetric matrix in his Eigenvalues and eigenvectors study. His work in Matrix addresses issues such as Singular value decomposition, which are connected to fields such as Singular value.

He most often published in these fields:

  • Applied mathematics (31.38%)
  • Mathematical analysis (25.80%)
  • Eigenvalues and eigenvectors (19.95%)

What were the highlights of his more recent work (between 2005-2011)?

  • Applied mathematics (31.38%)
  • Matrix (18.09%)
  • Combinatorics (14.63%)

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

Gene H. Golub mainly investigates Applied mathematics, Matrix, Combinatorics, Eigenvalues and eigenvectors and Pure mathematics. The study incorporates disciplines such as Iterative method, Mathematical optimization, Numerical analysis, Hermitian matrix and Least squares in addition to Applied mathematics. His work carried out in the field of Least squares brings together such families of science as Singular value, Singular value decomposition, Diagonal and Rank.

His Matrix research includes elements of Quadratic form, Computation, Standard algorithms and Google matrix. His Combinatorics study combines topics in areas such as Weight function and Block matrix. Gene H. Golub interconnects Rate of convergence, Defective matrix, Mathematical analysis and Symmetric matrix in the investigation of issues within Eigenvalues and eigenvectors.

Between 2005 and 2011, his most popular works were:

  • Symmetric Tensors and Symmetric Tensor Rank (435 citations)
  • Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems (289 citations)
  • Matrices, Moments and Quadrature with Applications (193 citations)

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

  • Statistics
  • Eigenvalues and eigenvectors
  • Mathematical analysis

Gene H. Golub mainly focuses on Applied mathematics, Hermitian matrix, Matrix, Numerical analysis and Eigenvalues and eigenvectors. His Applied mathematics research is multidisciplinary, relying on both Saddle point, Iterative method, Conjugate gradient method, System of linear equations and Numerical linear algebra. His Matrix study integrates concerns from other disciplines, such as Diagonal, Singular value decomposition, Rank, Power iteration and Least squares.

His research in Numerical analysis intersects with topics in Condition number, Linear subspace, Combinatorics and Search algorithm. His Eigenvalues and eigenvectors research incorporates themes from Mathematical analysis and Linear algebra. His Mathematical analysis research is multidisciplinary, incorporating elements of Rate of convergence and Quadrature.

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.

Top Publications

Matrix computations (3rd ed.)

Gene H. Golub;Charles F. Van Loan.
(1996)

13042 Citations

Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter

Gene H. Golub;Michael Heath;Grace Wahba.
Technometrics (1979)

4018 Citations

Singular value decomposition and least squares solutions

G. H. Golub;C. Reinsch.
Numerische Mathematik (1970)

3492 Citations

Numerical solution of saddle point problems

Michele Benzi;Gene H. Golub;Jörg Liesen.
Acta Numerica (2005)

2288 Citations

An Analysis of the Total Least Squares Problem

Gene H. Golub;Charles Van Loan.
SIAM Journal on Numerical Analysis (1980)

2164 Citations

Calculating the Singular Values and Pseudo-Inverse of a Matrix

G. Golub;W. Kahan.
Journal of The Society for Industrial and Applied Mathematics, Series B: Numerical Analysis (1965)

2056 Citations

Calculation of Gauss quadrature rules

Gene H. Golub;John H. Welsch.
Mathematics of Computation (1967)

1876 Citations

The differentiation of pseudoinverses and nonlinear least squares problems whose variables separate.

Gene H. Golub;Victor Pereyra.
SIAM Journal on Numerical Analysis (1972)

1604 Citations

A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration

Tony F. Chan;Gene H. Golub;Pep Mulet.
SIAM Journal on Scientific Computing (1999)

1022 Citations

Numerical methods for solving linear least squares problems

Gene Howard Golub.
Numerische Mathematik (1965)

1009 Citations

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

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