Science Explorer Interactive view Map

Mathematical Approximation and Integration

Mathematical Approximation and Integration is a research topic within Numerical Analysis. Science Explorer counts 10k research works in it since 1950. 13.4% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on high-dimensional integration techniques, particularly emphasizing the use of Quasi-Monte Carlo methods, lattice rules, and randomized approaches for multivariate approximation. The research also delves into applications in spherical crystals, discrepancy minimization, and the tractability of numerical integration in weighted spaces.

  • Quasi-Monte Carlo
  • High-dimensional Integration
  • Lattice Rules
  • Multivariate Approximation
  • Randomized Methods
  • Spherical Crystals
  • Discrepancy Minimization
  • Tractability
  • Weighted Spaces
  • Numerical Integration
Research works
10k
fractional, since 1950
In the world top 10%
1.4k
per year above
Top-10% rate
13.4%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
+6%
the tick is no change

Which countries lead Mathematical Approximation and Integration research?

By volume, the United States and China publish the most (171 and 150 works in 2022–2025).

By volume, 2022–2025

  1. 1 United States 171 works
  2. 2 China 150 works
  3. 3 Russia 134 works
  4. 4 India 109 works
  5. 5 Türkiye 86 works
  6. 6 Germany 72 works
  7. 7 Ukraine 53 works
  8. 8 France 48 works
  9. 9 United Kingdom 40 works
  10. 10 Japan 36 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.

United States: 19.0%China: 16.7%Russia: 14.9%India: 12.2%6 others listed: 37.2%19%largest
United States171 · 19.0%China150 · 16.7%Russia134 · 14.9%India109 · 12.2%6 others listed335 · 37.2%

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

Which institutions lead Mathematical Approximation and Integration research?

By volume in 2022–2025, Lomonosov Moscow State University publishes the most Mathematical Approximation and Integration research, followed by Institute of Mathematics and Lesya Ukrainka Volyn National University.

Who are the leading researchers in Mathematical Approximation and Integration?

The most-cited researchers publishing on Mathematical Approximation and Integration include Terence Tao.

  1. 1 Terence Tao United States 3.1k citations

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

Where is Mathematical Approximation and Integration research done?

The largest centres of Mathematical Approximation and Integration research in 2022–2025 are Moscow (Russia), Beijing (China), Sofia (Bulgaria) and Kyiv (Ukraine). Among places with at least 20 works in it, it is an unusually large share of all research in Sofia.

Largest cities, 2022–2025

  1. 1 Moscow Russia 71 works
  2. 2 Beijing China 29 works
  3. 3 Sofia Bulgaria 25 works
  4. 4 Kyiv Ukraine 24 works
  5. 5 Ankara Türkiye 19 works
  6. 6 Paris France 18 works
  7. 7 Tokyo Japan 16 works
  8. 8 Shanghai China 12 works
  9. 9 Linz Austria 11 works
  10. 10 Saint Petersburg Russia 11 works

Where it is the local speciality

  1. SofiaBG · 24.8 works17×
← less than its size predictsmore →

Location quotient: how much more of its research is in Mathematical Approximation and Integration than the world average.

See Mathematical Approximation and Integration on the map

Where is the best place to study Mathematical Approximation and Integration?

Among universities, judged by research, Lesya Ukrainka Volyn National University, Lomonosov Moscow State University and Johannes Kepler University of Linz 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 17.2%fractional works in this node (log) →share in the world top 10% →Lesya Ukrainka Volyn National University: 10, 43.9%Lomonosov Moscow State University: 21, 7.0%Johannes Kepler University of Linz: 8, 17.9%Tripura University: 8, 0.0%Lesya Ukrainka Volyn…Johannes Kepler Univ…Lomonosov Moscow Sta…Tripura University
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1 Lesya Ukrainka Volyn National UniversityUkraine 48.343.9%106.0×10 +296.9%
2 Lomonosov Moscow State UniversityRussia 37.97.0%18.6×21 +37.7%
3 Johannes Kepler University of LinzAustria 21.817.9%39.7×8 -4.3%
4 Tripura UniversityIndia 7.90.0%149.7×8

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is Mathematical Approximation and Integration research growing?

Output in 2018–2022 was 6% higher than in 2013–2017, peaking in 2024. The fastest-growing topics are Mathematical Approximation and Integration.

19801990200020102020
grewheldshrank

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

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.