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 52 Citations 14,273 159 World Ranking 480 National Ranking 245
Engineering and Technology D-index 50 Citations 11,982 153 World Ranking 1491 National Ranking 628

Research.com Recognitions

Awards & Achievements

2015 - SIAM Fellow For contributions to optimal control, optimization theory, and numerical optimization algorithms.

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Eigenvalues and eigenvectors
  • Algebra

His main research concerns Optimal control, Mathematical optimization, Mathematical analysis, Applied mathematics and Conjugate gradient method. William W. Hager has researched Optimal control in several fields, including Lagrange multiplier, Adjoint equation and Lipschitz continuity. His work deals with themes such as Function and Quadratic equation, which intersect with Mathematical optimization.

His Mathematical analysis study incorporates themes from Generalized inverse, State-transition matrix and Invertible matrix. His Applied mathematics study combines topics in areas such as Ordinary differential equation, Explicit and implicit methods, Calculus and Discontinuous Galerkin method. William W. Hager interconnects Line search, Gradient method and Stationary point in the investigation of issues within Conjugate gradient method.

His most cited work include:

  • Updating the inverse of a matrix (753 citations)
  • A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search (646 citations)
  • Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate (518 citations)

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

William W. Hager spends much of his time researching Optimal control, Applied mathematics, Mathematical optimization, Mathematical analysis and Rate of convergence. His Optimal control research is multidisciplinary, incorporating perspectives in Discretization, Lagrange multiplier, Collocation method and Collocation. His biological study spans a wide range of topics, including Separable space, Polynomial, Interval and Combinatorics.

William W. Hager combines subjects such as Nonlinear programming and Active set method with his study of Mathematical optimization. The study incorporates disciplines such as Pseudospectral optimal control and Legendre pseudospectral method in addition to Gauss pseudospectral method. His Constrained optimization research is multidisciplinary, incorporating elements of Augmented Lagrangian method and Conjugate gradient method.

He most often published in these fields:

  • Optimal control (29.82%)
  • Applied mathematics (27.98%)
  • Mathematical optimization (27.06%)

What were the highlights of his more recent work (between 2015-2021)?

  • Applied mathematics (27.98%)
  • Optimal control (29.82%)
  • Collocation method (8.72%)

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

William W. Hager mainly focuses on Applied mathematics, Optimal control, Collocation method, Rate of convergence and Collocation. His studies deal with areas such as Structure, Separable space, Nonlinear programming and Boundary value problem as well as Applied mathematics. William W. Hager conducts interdisciplinary study in the fields of Optimal control and Gauss through his works.

Many of his studies on Rate of convergence involve topics that are commonly interrelated, such as Algorithm. The various areas that he examines in his Polyhedron study include Mathematical optimization and Projection. His Mathematical optimization research includes elements of Line search and Sparse approximation.

Between 2015 and 2021, his most popular works were:

  • Convergence Rate for a Gauss Collocation Method Applied to Unconstrained Optimal Control (51 citations)
  • Adaptive Mesh Refinement Method for Optimal Control Using Decay Rates of Legendre Polynomial Coefficients (36 citations)
  • Convergence rate for a Gauss collocation method applied to constrained optimal control (31 citations)

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

  • Mathematical analysis
  • Eigenvalues and eigenvectors
  • Algebra

His primary areas of investigation include Orthogonal collocation, Applied mathematics, Optimal control, Gaussian quadrature and Rate of convergence. He applies his multidisciplinary studies on Applied mathematics and Gauss in his research. His research integrates issues of Polynomial and Collocation method in his study of Optimal control.

As a part of the same scientific study, he usually deals with the Polynomial, concentrating on Legendre polynomials and frequently concerns with Mathematical optimization. The concepts of his Mathematical optimization study are interwoven with issues in Nonlinear programming and Degree of a polynomial. His Rate of convergence course of study focuses on Algorithm and Iterated function, Matrix, Ergodic theory and Variational inequality.

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

Updating the inverse of a matrix

W. W. Hager.
Siam Review (1989)

1049 Citations

A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search

William W. Hager;Hongchao Zhang.
Siam Journal on Optimization (2005)

987 Citations

A SURVEY OF NONLINEAR CONJUGATE GRADIENT METHODS

William W. Hager;Hongchao Zhang.
(2005)

927 Citations

Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate

Yanqing Chen;Timothy A. Davis;William W. Hager;Sivasankaran Rajamanickam.
ACM Transactions on Mathematical Software (2008)

745 Citations

Brief paper: A unified framework for the numerical solution of optimal control problems using pseudospectral methods

Divya Garg;Michael Patterson;William W. Hager;Anil V. Rao.
Automatica (2010)

739 Citations

A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization

Hongchao Zhang;William W. Hager.
Siam Journal on Optimization (2004)

611 Citations

Runge-Kutta methods in optimal control and the transformed adjoint system

William W. Hager.
Numerische Mathematik (2000)

478 Citations

An hp‐adaptive pseudospectral method for solving optimal control problems

Christopher L. Darby;William W. Hager;Anil V. Rao.
Optimal Control Applications & Methods (2011)

402 Citations

Error estimates for the finite element solution of variational inequalities

Franco Brezzi;William W. Hager;P. A. Raviart.
Numerische Mathematik (1978)

385 Citations

Applied Numerical Linear Algebra

William W. Hager.
(1987)

376 Citations

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