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Topic · Computational Theory and Mathematics

Numerical Methods and Algorithms

Numerical Methods and Algorithms is a research topic within Computational Theory and Mathematics. Science Explorer counts 18k 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 the theory, implementation, and optimization of floating-point arithmetic for scientific computation. It covers topics such as interval analysis, high-precision computation, hardware implementation on FPGAs, numerical verification methods, decimal floating-point arithmetic, accuracy optimization, Taylor models, and handling interval uncertainty.

  • Floating-Point Arithmetic
  • Interval Analysis
  • High-Precision Computation
  • Hardware Implementation
  • Numerical Verification Methods
  • FPGA Acceleration
  • Decimal Floating-Point
  • Accuracy-Guaranteed Bit-Width Optimization
  • Taylor Models
  • Interval Uncertainty
Research works
18k
fractional, since 1950
In the world top 10%
1.8k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+10%
the tick is no change
Largest producer
China
23% of the 10 largest, 2022-now
Numerical Methods and Algorithms

Which countries lead Numerical Methods and Algorithms research?

By volume, China and the United States publish the most (355 and 349 works in 2022-now).

By volume, 2022-now

  1. 1 China 355 works
  2. 2 United States 349 works
  3. 3 India 334 works
  4. 4 Germany 104 works
  5. 5 France 100 works
  6. 6 Japan 74 works
  7. 7 Russia 71 works
  8. 8 United Kingdom 60 works
  9. 9 Italy 60 works
  10. 10 Canada 46 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: 22.9%United States: 22.5%India: 21.5%Germany: 6.7%6 others listed: 26.4%23%largest
China355 · 22.9%United States349 · 22.5%India334 · 21.5%Germany104 · 6.7%6 others listed410 · 26.4%

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

Which institutions lead Numerical Methods and Algorithms research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Numerical Methods and Algorithms research, followed by Chinese Academy of Sciences and National University of Defense Technology.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 33 works
  2. 2 Chinese Academy of SciencesChina 22 works
  3. 3 National University of Defense TechnologyChina 19 works
  4. 4 Indian Institute of Technology KharagpurIndia 18 works
  5. 5 Russian Academy of SciencesRussia 14 works
  6. 6 Amrita Vishwa VidyapeethamIndia 13 works
  7. 7 Tsinghua UniversityChina 12 works
  8. 8 Vellore Institute of Technology UniversityIndia 11 works
  9. 9 Charles UniversityCzechia 10 works
  10. 10 University of Electronic Science and Technology of ChinaChina 10 works

Who are the leading researchers in Numerical Methods and Algorithms?

The most-cited researchers publishing on Numerical Methods and Algorithms include Yoshua Bengio and Stephen M. Smith.

  1. 1 Yoshua Bengio Canada 476k citations
  2. 2 Stephen M. Smith United Kingdom 214k 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 Numerical Methods and Algorithms?

The most cited paper in Numerical Methods and Algorithms is "On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming" (Andreas Wächter, Lorenz T. Biegler, 2005), with 9,722 citations. Next come "Mersenne twister" (5,805) and "The Design and Implementation of FFTW3" (5,208).

Most cited papers
#PaperReleasedCitations
1 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
2 Mersenne twister Makoto Matsumoto, Takuji Nishimura · ACM Transactions on Modeling and Computer Simulation 1998 5,805
3 The Design and Implementation of FFTW3 Matteo Frigo, Steven G. Johnson · Proceedings of the IEEE 24 Jan 2005 5,208
4 LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares Christopher C. Paige, Michael A. Saunders · ACM Transactions on Mathematical Software Open access Mar 1982 4,448
5 Algorithm 778: L-BFGS-B Ciyou Zhu, Richard H. Byrd, Peihuang Lu et al. · ACM Transactions on Mathematical Software Open access Dec 1997 3,560
All 98 most cited papers, with filters and sorting

Where is Numerical Methods and Algorithms research done?

The largest centres of Numerical Methods and Algorithms research in 2022-now are Beijing (China), Bengaluru (India), Moscow (Russia) and Paris (France). Among places with at least 20 works in it, it is an unusually large share of all research in Hyderabad and Coimbatore.

Largest cities, 2022-now

  1. 1 BeijingChina 71 works
  2. 2 BengaluruIndia 30 works
  3. 3 MoscowRussia 28 works
  4. 4 ParisFrance 28 works
  5. 5 ChangshaChina 27 works
  6. 6 ShanghaiChina 27 works
  7. 7 NanjingChina 23 works
  8. 8 HyderabadIndia 22 works
  9. 9 TokyoJapan 21 works
  10. 10 ChennaiIndia 21 works

Where it is the local speciality

  1. HyderabadIN · 22.4 works5.5×
  2. CoimbatoreIN · 20.2 works5.4×
← less than its size predicts1×more →

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

See Numerical Methods and Algorithms on the map

Where is the best place to study Numerical Methods and Algorithms?

Among universities, judged by research, National University of Defense Technology, International Institute of Information Technology Bangalore and Indian Institute of Technology Kharagpur 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%10%20%mean 9.33%fractional works in this field (log) →share of work in the world top 10% →International Instit…Amrita Vishwa Vidyap…National University …Indian Institute of …
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
1National University of Defense TechnologyChina 65.811.1%13.0×19 +273.2%
2International Institute of Information Technology BangaloreIndia 61.420.5%57.6×8 +365.0%
3Indian Institute of Technology KharagpurIndia 60.05.2%19.0×18 +346.5%
4Amrita Vishwa VidyapeethamIndia 56.211.6%13.4×13 +19.3%
5Charles UniversityCzechia 55.58.9%11.5×10 +38.1%
6Tsinghua UniversityChina 54.819.5%2.7×12 +104.5%
7Vellore Institute of Technology UniversityIndia 36.712.2%6.2×11 -17.7%
8University of Electronic Science and Technology of ChinaChina 26.02.6%4.6×10 +104.9%
9The University of Texas at El PasoUnited States 22.70.0%30.5×8 +6.8%
10SRM Institute of Science and TechnologyIndia 20.01.7%4.5×9 +51.4%

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 Numerical Methods and Algorithms, country by country

Is Numerical Methods and Algorithms research growing?

Output in 2022-2025 was 10% higher than in 2018-2021, peaking in 2002. The fastest-growing topics are Numerical Methods 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 Numerical Methods and Algorithms as a percentage of every work published that year, 0.0076% in 2024.

still counting0.020%0.040%0.060%Numerical Methods and Algorithms0.010% in 202519801990200020102020

Fractional works of Numerical Methods 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%Numerical Methods and Algorithms10.4% 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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