World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
53
Citations
27237
World Ranking
869
National Ranking
418

Engineering and Technology

D-Index
53
Citations
27289
World Ranking
3301
National Ranking
969

Richard H. Byrd publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Richard H. Byrd sits on this spectrum.

42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 83 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 publications 537+

This scientist: 123 publications — 22nd percentile

22% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

Richard H. Byrd D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Richard H. Byrd sits on this spectrum.

30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 138 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 53 D-Index — 76th percentile

76% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

Research.com Recognitions

  • 2020 - SIAM Fellow For fundamental contributions to the theory and algorithms for nonlinear optimization.

Overview

Richard H. Byrd is affiliated with the University of Colorado Boulder in the United States. Their research primarily addresses topics within Mathematics and Computer Science, encompassing both main and subfields related to numerical and computational methods.

The main fields of study covered in their work include:

  • Mathematics
  • Computer Science

Within subfields of study, their research focuses on:

  • Numerical Analysis
  • Computational Theory and Mathematics

The topics frequently explored in their publications are:

  • Advanced Optimization Algorithms Research
  • Iterative Methods for Nonlinear Equations
  • Optimization and Variational Analysis

One recent paper authored in collaboration with Yuchen Xie is titled "Analysis of the BFGS Method with Errors", published in 2020 in the SIAM Journal on Optimization. This work has been cited 29 times. The SIAM Journal on Optimization also represents a frequent publication venue for their research.

Their coauthors include:

  • Yuchen Xie
  • Jorge Nocedal

Richard H. Byrd's contributions have been recognized with the award of SIAM Fellow in 2020 for fundamental contributions to the theory and algorithms for nonlinear optimization.

Best Publications

  • A limited memory algorithm for bound constrained optimization

    Richard H. Byrd;Peihuang Lu;Jorge Nocedal;Ciyou Zhu

  • Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization

    Ciyou Zhu;Richard H. Byrd;Peihuang Lu;Jorge Nocedal

  • An Interior Point Algorithm for Large-Scale Nonlinear Programming

    Richard H. Byrd;Mary E. Hribar;Jorge Nocedal

  • A trust region method based on interior point techniques for nonlinear programming

    Richard H. Byrd;Jean Charles Gilbert;Jorge Nocedal

  • Knitro: An Integrated Package for Nonlinear Optimization

    Richard H. Byrd;Jorge Nocedal;Richard A. Waltz

  • Representations of quasi-Newton matrices and their use in limited memory methods

    Richard H. Byrd;Jorge Nocedal;Robert B. Schnabel

  • Approximate solution of the trust region problem by minimization over two-dimensional subspaces

    Richard H. Byrd;Robert B. Schnabel;Gerald A. Shultz

  • A Stochastic Quasi-Newton Method for Large-Scale Optimization

    Richard H. Byrd;S. L. Hansen;Jorge Nocedal;Yoram Singer

  • A tool for the analysis of Quasi-Newton methods with application to unconstrained minimization

    Richard H. Byrd;Jorge Nocedal

  • A Trust Region Algorithm for Nonlinearly Constrained Optimization

    Richard H. Byrd;Robert B. Schnabel;Gerald A. Shultz

  • A Stable and Efficient Algorithm for Nonlinear Orthogonal Distance Regression

    Paul T. Boggs;Richard H. Byrd;Robert B. Schnabel

  • Global Convergence of a Cass of Quasi-Newton Methods on Convex Problems

    Richard H. Byrd;Jorge Nocedal;Ya-Xiang Yuan

  • Sample size selection in optimization methods for machine learning

    Richard H. Byrd;Gillian M. Chin;Jorge Nocedal;Yuchen Wu

  • A Family of Trust Region Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties.

    Gerald A. Shultz;Robert B. Schnabel;Richard H. Byrd

  • Algorithm 676: ODRPACK: software for weighted orthogonal distance regression

    Paul T. Boggs;Janet R. Donaldson;Richaard h. Byrd;Robert B. Schnabel

  • ON THE USE OF STOCHASTIC HESSIAN INFORMATION IN OPTIMIZATION METHODS FOR MACHINE LEARNING

    Richard H. Byrd;Gillian M. Chin;Will Neveitt;Jorge Nocedal

  • User's reference guide for ODRPACK version 2.01:: software for weighted orthogonal distance regression

    Paul T Boggs;Richard H Byrd;Janet E Rogers;Robert B Schnabel

  • An algorithm for nonlinear optimization using linear programming and equality constrained subproblems

    Richard H. Byrd;Nicholas I. M. Gould;Jorge Nocedal;Richard A. Waltz

  • Exact and inexact subsampled Newton methods for optimization

    Raghu Bollapragada;Richard H. Byrd;Jorge Nocedal

  • A limited-memory algorithm for bound-constrained optimization

    R.H. Byrd;L. Peihuang;J. Nocedal

  • A Family of Trust Region Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties ; CU-CS-216-82

    Gerald A Shultz;Robert B Schnabel;Richard H Byrd

  • A Trust Region Algorithm for Nonlinearly Constrained Optimization ; CU-CS-313-85

    Richard H Byrd;Robert B Schnabel;Gerald A Shultz

  • Approximate Solution of the Trust Region Problem by Minimization over Two-Dimensional Subspaces ; CU-CS-346-86

    Richard H Byrd;Robert B Schnabel;Gerald A Schultz

Frequent Co-Authors

Robert B. Schnabel
Robert B. Schnabel University of Colorado Boulder
Jorge Nocedal
Jorge Nocedal Northwestern University
Teresa Head-Gordon
Teresa Head-Gordon University of California, Berkeley
Nicholas I. M. Gould
Nicholas I. M. Gould Rutherford Appleton Laboratory
André van der Hoek
André van der Hoek University of California, Irvine
Tim Curran
Tim Curran University of Colorado Boulder
Xiao-Chuan Cai
Xiao-Chuan Cai University of Colorado Boulder
Yin Zhang
Yin Zhang Chinese University of Hong Kong, Shenzhen
Ya-xiang Yuan
Ya-xiang Yuan Chinese Academy of Sciences

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