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Topic · Computational Theory and Mathematics

Matrix Theory and Algorithms

Matrix Theory and Algorithms is a research topic within Computational Theory and Mathematics. Science Explorer counts 50k research works in it since 1950. 10.0% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on matrix algorithms, iterative methods, and numerical techniques for solving eigenvalue problems, preconditioning sparse linear systems, and addressing saddle point problems. It covers topics such as Krylov subspace methods, structured preconditioners, parallel computing, and numerical linear algebra.

  • Matrix Computations
  • Numerical Linear Algebra
  • Preconditioning Techniques
  • Iterative Methods
  • Eigenvalue Problems
  • Sparse Linear Systems
  • Krylov Subspace Methods
  • Saddle Point Problems
  • Structured Preconditioners
  • Parallel Computing
Research works
50k
fractional, since 1950
In the world top 10%
5k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+15%
the tick is no change
Largest producer
China
35% of the 10 largest, 2022-now
Matrix Theory and Algorithms

Which countries lead Matrix Theory and Algorithms research?

By volume, China and the United States publish the most (1.4k and 824 works in 2022-now).

By volume, 2022-now

  1. 1 China 1.4k works
  2. 2 United States 824 works
  3. 3 India 401 works
  4. 4 Germany 294 works
  5. 5 Russia 244 works
  6. 6 France 193 works
  7. 7 Italy 167 works
  8. 8 Japan 165 works
  9. 9 United Kingdom 155 works
  10. 10 Iran 141 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 35.5%United States: 20.6%India: 10.0%Germany: 7.3%6 others listed: 26.6%35%largest
China1,421 · 35.5%United States824 · 20.6%India401 · 10.0%Germany294 · 7.3%6 others listed1,066 · 26.6%

Shares of the rows listed above, not of the whole node.

Which institutions lead Matrix Theory and Algorithms research?

By volume in 2022-now, Russian Academy of Sciences publishes the most Matrix Theory and Algorithms research, followed by Centre National de la Recherche Scientifique and Chinese Academy of Sciences.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 79 works
  2. 2 Centre National de la Recherche ScientifiqueFrance 72 works
  3. 3 Chinese Academy of SciencesChina 42 works
  4. 4 University of NisSerbia 37 works
  5. 5 University of SfaxTunisia 33 works
  6. 6 Shanghai UniversityChina 33 works
  7. 7 Technical University of MunichGermany 32 works
  8. 8 Lomonosov Moscow State UniversityRussia 26 works
  9. 9 Southeast UniversityChina 25 works
  10. 10 National Academy of Sciences of UkraineUkraine 22 works

Who are the leading researchers in Matrix Theory and Algorithms?

The most-cited researchers publishing on Matrix Theory and Algorithms include Donald B. Rubin, Trevor Hastie and Gordon K. Smyth.

  1. 1 Donald B. Rubin United States 301k citations
  2. 2 Trevor Hastie United States 301k citations
  3. 3 Gordon K. Smyth Australia 237k citations
  4. 4 Peter M. Bentler United States 233k citations
  5. 5 Donald G. Truhlar United States 230k citations
  6. 6 A. Meyer France 224k citations
  7. 7 Kai You Wang China 224k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Matrix Theory and Algorithms?

The most cited paper in Matrix Theory and Algorithms is "LINCS: A linear constraint solver for molecular simulations" (Berk Hess, Henk Bekker, Herman J. C. Berendsen et al., 1997), with 17,504 citations. Next come "An Index of Factorial Simplicity" (14,788) and "On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming" (9,722).

Most cited papers
#PaperReleasedCitations
1 LINCS: A linear constraint solver for molecular simulations Berk Hess, Henk Bekker, Herman J. C. Berendsen et al. · Journal of Computational Chemistry Sep 1997 17,504
2 An Index of Factorial Simplicity Henry F. Kaiser · Psychometrika Mar 1974 14,788
3 On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming Andreas Wächter, Lorenz T. Biegler · Mathematical Programming 28 Apr 2005 9,722
4 On the limited memory BFGS method for large scale optimization Dong C. Liu, Jorge Nocedal · Mathematical Programming Aug 1989 8,813
5 A Limited Memory Algorithm for Bound Constrained Optimization Richard H. Byrd, Peihuang Lu, Jorge Nocedal et al. · SIAM Journal on Scientific Computing Sep 1995 6,417
All 99 most cited papers, with filters and sorting

Where is Matrix Theory and Algorithms research done?

The largest centres of Matrix Theory and Algorithms research in 2022-now are Beijing (China), Shanghai (China), Moscow (Russia) and Xi'an (China). Among places with at least 20 works in it, it is an unusually large share of all research in Niš and Sfax.

Largest cities, 2022-now

  1. 1 BeijingChina 168 works
  2. 2 ShanghaiChina 125 works
  3. 3 MoscowRussia 110 works
  4. 4 Xi'anChina 70 works
  5. 5 NanjingChina 69 works
  6. 6 TokyoJapan 54 works
  7. 7 ParisFrance 48 works
  8. 8 GuangzhouChina 47 works
  9. 9 MunichGermany 43 works
  10. 10 ChangshaChina 42 works

Where it is the local speciality

  1. NišRS · 36.8 works38×
  2. SfaxTN · 32.8 works15×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Matrix Theory and Algorithms than the world average.

See Matrix Theory and Algorithms on the map

Where is the best place to study Matrix Theory and Algorithms?

Among universities, judged by research, Shanghai University, University of Jordan and University of Nis score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 24.14%fractional works in this field (log) →share of work in the world top 10% →Shanghai UniversityJadavpur UniversityUniversity of JordanUniversity of Nis
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Shanghai UniversityChina 87.640.0%8.6×33 +15.0%
2University of JordanJordan 72.626.4%10.3×15 +303.7%
3University of NisSerbia 69.412.1%42.0×37 +15.1%
4Jadavpur UniversityIndia 67.733.8%9.3×14 +126.3%
5Shahid Beheshti UniversityIran 63.527.6%9.7×12 +39.5%
6University of SfaxTunisia 61.46.8%24.9×33 +115.0%
7Liaocheng UniversityChina 60.330.1%14.0×13 +36.8%
8École Polytechnique Fédérale de LausanneSwitzerland 59.829.2%5.4×12 +150.3%
9University of OxfordUnited Kingdom 58.312.2%3.0×22 +109.4%
10Fudan UniversityChina 55.523.2%2.1×17 +58.0%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Matrix Theory and Algorithms, country by country

Is Matrix Theory and Algorithms research growing?

Output in 2022-2025 was 15% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Matrix Theory and Algorithms.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Matrix Theory and Algorithms as a percentage of every work published that year, 0.028% in 2024.

still counting0.050%0.10%0.15%Matrix Theory and Algorithms0.027% in 202519801990200020102020

Fractional works of Matrix Theory and Algorithms over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Matrix Theory and Algorithms10.0% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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