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. 10.1% 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%
- 1k per year above
- Top-10% rate
- 10.1% share of its works in the world top 10%
- Growth, 2018-21 → 2022-25
- +11% the tick is no change
- Largest producer
United States
20% of the 10 largest, 2022-now
Which countries lead Mathematical Approximation and Integration research?
By volume, the United States and China publish the most (195 and 173 works in 2022-now).
By volume, 2022-now
- 1
United States
195 works
- 2
China
173 works
- 3
Russia
148 works
- 4
India
113 works
- 5
Türkiye
88 works
- 6
Germany
82 works
- 7
Ukraine
56 works
- 8
France
53 works
- 9
United Kingdom
45 works
- 10
Japan
40 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.
Shares of the rows listed above, not of the whole node.
Which institutions lead Mathematical Approximation and Integration research?
By volume in 2022-now, Russian Academy of Sciences publishes the most Mathematical Approximation and Integration research, followed by Centre National de la Recherche Scientifique and Lomonosov Moscow State University.
By volume, 2022-now
- 1
Russian Academy of SciencesRussia
49 works
- 2
Centre National de la Recherche ScientifiqueFrance
24 works
- 3
Lomonosov Moscow State UniversityRussia
23 works
- 4
National Academy of Sciences of UkraineUkraine
21 works
- 5
Bulgarian Academy of Sciences
Bulgaria
20 works
- 6
Lesya Ukrainka Volyn National UniversityUkraine
10 works
- 7
Johannes Kepler University of Linz
Austria
10 works
- 8
St Petersburg UniversityRussia
9 works
- 9
Tripura UniversityIndia
8 works
- 10
Stanford UniversityUnited States
8 works
Who are the leading researchers in Mathematical Approximation and Integration?
The most-cited researchers publishing on Mathematical Approximation and Integration include R. W. L. Jones, H. Vincent Poor and David L. Donoho.
- 1
R. W. L. Jones
United Kingdom
189k citations
- 2
H. Vincent Poor
United States
165k citations
- 3
David L. Donoho
United States
154k citations
- 4
Bernhard Schölkopf
Germany
148k 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-now 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-now
Where it is the local speciality
- SofiaBG · 25.5 works16×
Location quotient: how much more of its research is in Mathematical Approximation and Integration than the world average.
Where is the best place to study Mathematical Approximation and Integration?
Among universities, judged by research, Lomonosov Moscow State University, Lesya Ukrainka Volyn National 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.
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.
| # | University | Score | Top 10% | Specialisation | Works | Growth |
|---|---|---|---|---|---|---|
| 1 | Lomonosov Moscow State UniversityRussia |
52.4 | 6.2% | 20.8× | 23 | +19.3% |
| 2 | Lesya Ukrainka Volyn National UniversityUkraine |
45.9 | 39.7% | 118.0× | 10 | -24.0% |
| 3 | Johannes Kepler University of LinzAustria |
32.9 | 17.3% | 43.9× | 10 | +1.6% |
| 4 | Tripura UniversityIndia |
19.8 | 8.3% | 155.7× | 8 | +151.7% |
| 5 | St Petersburg UniversityRussia |
2.4 | 4.6% | 14.0× | 9 | -45.2% |
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 Mathematical Approximation and Integration, country by countryIs Mathematical Approximation and Integration research growing?
Output in 2022-2025 was 11% higher than in 2018-2021, peaking in 2024. The fastest-growing topics are Mathematical Approximation and Integration.
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 Mathematical Approximation and Integration as a percentage of every work published that year, 0.0073% in 2024.
Fractional works of Mathematical Approximation and Integration 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.
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.
Discussion
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