Most cited papers in Mathematical Approximation and Integration
What are the most cited papers in Mathematical Approximation and Integration?
The most cited paper in Mathematical Approximation and Integration is "Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates" (Ilya M. Sobol, 2001), with 6,427 citations. Next come "Optimal approximations by piecewise smooth functions and associated variational problems" (5,245) and "Random Number Generation and Quasi-Monte Carlo Methods." (2,965).
Showing 50 of 100 papers. Every paper with more than 325 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates Ilya M. Sobol · Mathematics and Computers in Simulation | Feb 2001 | 6,427 |
| 2 | Optimal approximations by piecewise smooth functions and associated variational problems David B. Mumford, Jayant M. Shah · Communications on Pure and Applied Mathematics | Jul 1989 | 5,245 |
| 3 | Random Number Generation and Quasi-Monte Carlo Methods. Bruce Jay Collings, Harald Niederreiter · Journal of the American Statistical Association | Jun 1993 | 2,965 |
| 4 | Centroidal Voronoi Tessellations: Applications and Algorithms Qiang Du, Vance Faber, Max Gunzburger · SIAM Review | 1999 | 2,297 |
| 5 | On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals John H. Halton · Numerische Mathematik | Dec 1960 | 2,009 |
| 6 | Monte Carlo and quasi-Monte Carlo methods Russel E. Caflisch · Acta Numerica | 1998 | 1,778 |
| 7 | A new algorithm for adaptive multidimensional integration G. Peter Lepage · Journal of Computational Physics | May 1978 | 1,677 |
| 8 | Multilevel Monte Carlo Path Simulation Michael B. Giles · Operations Research | Jun 2008 | 1,522 |
| 9 | Approximation of functional depending on jumps by elliptic functional via t‐convergence Luigi Ambrosio, Vincenzo Maria Tortorelli · Communications on Pure and Applied Mathematics | Dec 1990 | 1,483 |
| 10 | Splines minimizing rotation-invariant semi-norms in Sobolev spaces Jean Duchon · Lecture notes in mathematics | 1977 | 1,394 |
| 11 | A General Definition of Residuals David Roxbee Cox, E. J. Snell · Journal of the Royal Statistical Society Series B (Statistical Methodology) | Jul 1968 | 1,326 |
| 12 | On the approximate calculation of multiple integrals Nikolai Sergeevich Bakhvalov · Journal of Complexity | 2 Feb 2015 | 1,270 |
| 13 | On the ratio of optimal integral and fractional covers László Lovász · Discrete Mathematics | 1975 | 1,134 |
| 14 | Weighted norm inequalities for maximal functions and singular integrals Ronald R. Coifman, Charles Fefferman · Studia Mathematica | 1974 | 1,125 |
| 15 | Distributing many points on a sphere Edward Barry Saff, Arno B. J. Kuijlaars · The Mathematical Intelligencer | Dec 1997 | 1,108 |
| 16 | An approximation of partial sums of independent RV's, and the sample DF. II J. Koml�s, Péter Major, G. Tusn�dy · Probability Theory and Related Fields | 1976 | 1,025 |
| 17 | Spherical codes and designs P. Delsarte, J.-M. Goethals, J.J. Seidel · Geometriae Dedicata | Sep 1977 | 993 |
| 18 | Cuba—a library for multidimensional numerical integration Thomas H. Hahn · Computer Physics Communications | 19 Apr 2005 | 981 |
| 19 | Numerical integration using sparse grids Thomas V. Gerstner, Michael Griebel · Numerical Algorithms | 1998 | 930 |
| 20 | Uniform Design: Theory and Application Kai-Tai Fang, Dennis K. J. Lin, Peter Winker et al. · Technometrics | Aug 2000 | 897 |
| 21 | Monte Carlo methods for security pricing Phelim Boyle, Mark N. Broadie, Paul Glasserman · Journal of Economic Dynamics and Control | Jun 1997 | 879 |
| 22 | Algorithm 659 Paul Bratley, Bennett L. Fox · ACM Transactions on Mathematical Software | Mar 1988 | 867 |
| 23 | Simulation estimation of mixed discrete choice models using randomized and scrambled Halton sequences Chandra R. Bhat · Transportation Research Part B Methodological | 7 Apr 2003 | 864 |
| 24 | Minimax Theorems Ky Fan · Proceedings of the National Academy of Sciences | 1953 | 850 |
| 25 | Multilevel Monte Carlo methods Michael B. Giles · Acta Numerica | 27 Apr 2015 | 805 |
| 26 | An approximation of partial sums of independent RV'-s, and the sample DF. I J. Koml�s, Péter Major, G. Tusn�dy · Probability Theory and Related Fields | 1975 | 801 |
| 27 | Estimating Parameters in Continuous Univariate Distributions with a Shifted Origin Russell C. H. Cheng, N. A. K. Amin · Journal of the Royal Statistical Society Series B (Statistical Methodology) | Jul 1983 | 788 |
| 28 | Why the Monte Carlo method is so important today Dirk P. Kroese, Tim J. Brereton, Thomas Taimre et al. · Wiley Interdisciplinary Reviews Computational Statistics | 20 Jun 2014 | 758 |
| 29 | n-Widths in Approximation Theory. Klaus Höllig, Allan M. Pinkus · Mathematics of Computation | Oct 1986 | 748 |
| 30 | An Introduction to the Approximation of Functions Joseph W. Jerome, Theodore J. Rivlin · Technometrics | May 1970 | 737 |
| 31 | A generalized discrepancy and quadrature error bound Fred J. Hickernell · Mathematics of Computation | 1998 | 728 |
| 32 | Optimization of computer simulation models with rare events Reuven Y. Rubinstein · European Journal of Operational Research | May 1997 | 708 |
| 33 | Applications ofB-splines in atomic and molecular physics H. Bachau, E. Cormier, Piero Decleva et al. · Reports on Progress in Physics | 20 Nov 2001 | 702 |
| 34 | Solving Fredholm integrals of the first kind with tensor product structure in 2 and 2.5 dimensions Lalitha Venkataramanan, Yi‐Qiao Song, Martin D. Hürlimann · IEEE Transactions on Signal Processing | May 2002 | 688 |
| 35 | The Grand Tour: A Tool for Viewing Multidimensional Data Daniel Asimov · SIAM Journal on Scientific and Statistical Computing | 1985 | 661 |
| 36 | Quantum annealing: A new method for minimizing multidimensional functions A.B. Finnila, M.A. Gomez, C. Sebenik et al. · Chemical Physics Letters | Mar 1994 | 651 |
| 37 | Is Gauss Quadrature Better than Clenshaw–Curtis? Lloyd N. Trefethen · SIAM Review | 2008 | 646 |
| 38 | High dimensional polynomial interpolation on sparse grids Volker Barthelmann, Erich Novak, Klaus Ritter · Advances in Computational Mathematics | Mar 2000 | 644 |
| 39 | High-dimensional integration: The quasi-Monte Carlo way Josef Dick, Frances Y. Kuo, Ian H. Sloan · Acta Numerica | 2 Apr 2013 | 642 |
| 40 | Analysis of variance designs for model output Michiel J. W. Jansen · Computer Physics Communications | Mar 1999 | 640 |
| 41 | Spinor techniques for calculating Ronald H.P. Kleiss, W.J. Stirling · Nuclear Physics B | Dec 1985 | 637 |
| 42 | The influence of variables on Boolean functions J. Kahn, Gil Kalai, Nathan Linial | 1988 | 630 |
| 43 | When Are Quasi-Monte Carlo Algorithms Efficient for High Dimensional Integrals? Ian H. Sloan, Henryk Woźniakowski · Journal of Complexity | Mar 1998 | 628 |
| 44 | Tensor Regression with Applications in Neuroimaging Data Analysis Hua Zhou, Lexin Li, Hongtu Zhu · Journal of the American Statistical Association | 25 Mar 2013 | 578 |
| 45 | Point sets and sequences with small discrepancy Harald Niederreiter · Monatshefte für Mathematik | Dec 1987 | 569 |
| 46 | Some Approximation Theorems via Statistical Convergence Akif D. Gadjiev, Cihan Orhan · Rocky Mountain Journal of Mathematics | Mar 2002 | 555 |
| 47 | Dimension?Adaptive Tensor?Product Quadrature Thomas V. Gerstner, Michael Griebel · Computing | Aug 2003 | 552 |
| 48 | Monte Carlo theory and practice F. James · Reports on Progress in Physics | Sep 1980 | 545 |
| 49 | A guided tour of chernoff bounds Torben Hagerup, Christine Rüb · Information Processing Letters | Feb 1990 | 526 |
| 50 | MONTE CARLO METHODS FOR SOLVING MULTIVARIABLE PROBLEMS J. M. Hammersley · Annals of the New York Academy of Sciences | May 1960 | 524 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.