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Sobol’, Il’ya Meerovich

Author ID: sobol.ilya-m Recent zbMATH articles by "Sobol’, Il’ya Meerovich"
Published as: Sobol’, I. M.; Sobol, I. M.; Sobol’, Ilya M.; Sobol, Ilya M.; Sobol’, Il’ya
Further Spellings: Соболь Илья Меерович
External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef
Documents Indexed: 124 Publications since 1948, including 17 Books
Biographic References: 3 Publications
Co-Authors: 44 Co-Authors with 55 Joint Publications
871 Co-Co-Authors
all top 5

Serials

16 U.S.S.R. Computational Mathematics and Mathematical Physics
12 Matematicheskoe Modelirovanie
11 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
11 Monte Carlo Methods and Applications
7 Soviet Mathematics. Doklady
4 Mathematics and Computers in Simulation
3 Uspekhi Matematicheskikh Nauk [N. S.]
2 Computers & Mathematics with Applications
2 Computer Physics Communications
2 Theory of Probability and its Applications
2 Mathematical and Computer Modelling
2 Computational Mathematics and Mathematical Physics
2 Soviet Physics. Doklady
2 Doklady Akademii Nauk SSSR. Novaya Seriya
1 Doklady Akademii Nauk SSSR
1 Moscow University Mathematics Bulletin
1 Teoriya Veroyatnosteĭ i eë Primeneniya
1 Differentsial’nye Uravneniya
1 Differential Equations
1 Journal of Computational and Applied Mathematics
1 Journal of Number Theory
1 Matematicheskiĭ Sbornik. Novaya Seriya
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Sitzungsberichte. Abteilung II. Österreichische Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse
1 SIAM Journal on Numerical Analysis
1 Siberian Mathematical Journal
1 Sibirskiĭ Matematicheskiĭ Zhurnal
1 Surveys on Mathematics for Industry
1 Journal of Statistical Computation and Simulation
1 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika
1 Mathematical Modeling and Computational Experiment
1 Voprosy Vychislitel’noĭ i Prikladnoĭ Matematiki
1 Vychislitel’nye Tekhnologii
1 International Journal of Modern Physics C
1 Kleine Ergänzungsreihe zu den Hochschulbüchern für Mathematik

Publications by Year

Citations contained in zbMATH Open

87 Publications have been cited 1,686 times in 1,091 Documents Cited by Year
Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Zbl 1005.65004
Sobol’, I. M.
349
2001
Sensitivity estimates for nonlinear mathematical models. Zbl 1039.65505
Sobol’, I. M.
338
1993
On the distribution of points in a cube and the approximate evaluation of integrals. Zbl 0185.41103
Sobol’, I. M.
228
1969
On sensitivity estimation for nonlinear mathematical models. Zbl 0974.00506
Sobol’, I. M.
87
1990
Numerical Monte Carlo methods. (Численные методы Монте-Карло.) Zbl 0289.65001
Sobol’, I. M.
69
1973
Multidimensional quadrature formulas and Haar functions. (Многомерные квадратурные формулы и функции Хаара.) Zbl 0195.16903
Sobol’, I. M.
69
1969
Uniformly distributed sequences with an additional uniform property. Zbl 0391.10033
Sobol’, I. M.
67
1977
Derivative based global sensitivity measures and their link with global sensitivity indices. Zbl 1167.62005
Sobol’, I. M.; Kucherenko, S.
56
2009
Sensitivity measures, ANOVA-like techniques and the use of bootstrap. Zbl 1102.62335
Archer, G. E. B.; Saltelli, A.; Sobol, I. M.
35
1997
On the systematic search in a hypercube. Zbl 0445.65006
Sobol’, I. M.
33
1979
A primer for the Monte Carlo method. Transl. from the Russian. Zbl 0842.65002
Sobol’, I. M.
20
1994
A new derivative based importance criterion for groups of variables and its link with the global sensitivity indices. Zbl 1219.65005
Sobol’, I. M.; Kucherenko, S.
19
2010
Quasi-Monte Carlo methods for numerical integration: Comparison of different low discrepancy sequences. Zbl 0851.65015
Radović, Igor; Sobol’, Ilya M.; Tichy, Robert F.
18
1996
Monte Carlo estimators for small sensitivity indices. Zbl 1138.65004
Sobol’, I. M.; Myshetskaya, E. E.
18
2007
The Monte Carlo method. The method of statistical trials. Zbl 0139.35602
Busienko, N. P.; Golenko, D. I.; Shreider, Y. A.; Sobol’, I. M.; Sragovich, V. G.
17
1966
Uniformly distributed sequences with an additional uniform property. Zbl 0379.40003
Sobol’, I. M.
13
1976
Selection of optimal parameters in problems with several criteria. (Vybor optimal’nykh parametrov v zadachakh so mnogimi kriteriyami). Zbl 0666.93074
Sobol’, I. M.; Statnikov, R. B.
13
1981
On global sensitivity analysis of quasi-Monte Carlo algorithms. Zbl 1072.65004
Sobol’, I. M.; Kucherenko, S. S.
13
2005
Erratum to: “Global sensitivity indices for the investigation of nonlinear mathematical models”. Zbl 1140.60323
Sobol’, I. M.
13
2007
On the use of variance reducing multipliers in Monte Carlo computations of a global sensitivity index. Zbl 1018.65002
Sobol’, I. M.; Levitan, Yu. L.
11
1999
Calculation of improper integrals using uniformly distributed sequences. Zbl 0283.41016
Sobol’, I. M.
10
1973
Sensitivity analysis for nonlinear mathematical models: Numerical experiments. Zbl 0974.00507
Saltelli, A.; Sobol’, I. M.
9
1995
An efficient approach to multicriteria optimum design problems. Zbl 0749.90044
Sobol’, I. M.
9
1992
One more experiment on estimating high-dimensional integrals by quasi-Monte Carlo methods. Zbl 1018.65003
Sobol’, I. M.; Asotsky, D. I.
8
2003
A pseudo-random number generator for personal computers. Zbl 0949.65004
Sobol’, I. M.; Levitan, Yu. L.
6
1999
Integration with quasirandom sequences: Numerical experience. Zbl 0940.65502
Sobol’, Ilya M.; Shukhman, Boris V.
6
1995
On the crude multidimensional search. Zbl 0823.65058
Sobol’, Ilya M.; Bakin, Sergey G.
6
1994
Pseudo-random numbers for constructing discrete Markov chains by the Monte Carlo method. Zbl 0303.60059
Sobol’, I. M.
5
1975
The Monte Carlo method. Translated and adapted from the 2nd Russian edition by Robert Messer, John Stone, and Peter Fortini. Zbl 0309.65001
Sobol’, I. M.
5
1974
On a pseudo-random number generator for personal computers. Zbl 0974.65500
Levitan, Yu. L.; Sobol’, I. M.
5
1990
On quasirandom sequences for numerical computations. Zbl 0684.65006
Levitan, Yu. L.; Markovich, N. I.; Rozin, S. G.; Sobol’, I. M.
5
1988
On quasirandom sequences for numerical computations. Zbl 0653.65007
Levitan, Yu. L.; Markovich, N. I.; Rozin, S. G.; Sobol’, I. M.
5
1988
The use of \(\omega^ 2\)-distribution for error estimation in the calculation of integrals by the Monte Carlo method. Zbl 0123.33102
Sobol’, I. M.
5
1962
The method of statistical testing (the Monte Carlo method). Edited by Yu. A. Shreĭder. (Метод статистических испытаний (Метод Монте-Карло).) Zbl 0106.32802
Buslenko, N. P.; Golenko, D. I.; Sobol’, I. M.; Sragovich, V. G.; Shreĭder, Yu. A.
4
1962
Points, uniformly filling a multidimensional cube. (Tochki, ravnomerno zapolnyayushchie mnogomernyj kub). Zbl 0564.10001
Sobol’, I. M.
4
1985
Quasi-Monte Carlo: a high-dimensional experiment. Zbl 1305.11066
Sobol, Ilya M.; Shukhman, Boris V.
4
2014
Error estimates for the crude approximation of the trade-off curve. Zbl 0898.90115
Sobol’, I. M.; Levitan, Yu. L.
4
1997
A variance reducing multiplier for Monte Carlo integrations. Zbl 0858.65024
Sobol’, I. M.; Tutunnikov, A. V.
4
1996
Global sensitivity indices for the investigation of nonlinear mathematical models. Zbl 1089.26500
Sobol’, I. M.
4
2005
A new measure of irregularity of distribution. Zbl 0743.11039
Sobol’, Ilya M.; Nuzhdin, Oleg V.
4
1991
On global sensitivity indices: Monte Carlo estimates affected by random errors. Zbl 1124.65004
Sobol’, Ilya M.; Shukhman, Boris V.
4
2007
Convergence estimates for crude approximations of a Pareto set. Zbl 1047.90063
Sobol’, I. M.; Myshetskaya, E. E.
4
2002
Über das asymptotische Verhalten der Lösungen linearer Differentialgleichungen. Zbl 0038.25301
Sobol’, I. M.
4
1948
On average dimensions of particle transport estimators. Zbl 1499.65007
Sobol, Ilya M.; Shukhman, Boris V.
3
2018
A limit theorem for average dimensions. Zbl 1358.11091
Shukhman, Boris V.; Sobol, Ilya M.
3
2015
On functions satisfying a Lipschitz condition in multidimensional problems of computational mathematics. Zbl 0641.65014
Sobol’, I. M.
3
1987
Determination of the extremal values of a function of several variables satisfying a generalized Lipschitz condition. Zbl 0668.90070
Sobol’, I. M.
3
1988
Random and quasirandom sequences: Numerical estimates of uniformity of distribution. Zbl 0803.11042
Sobol’, I. M.; Shukman, B. V.
3
1993
Accurate estimate of the error of multidimensional quadrature formulas for functions of class \(S_ p\). Zbl 0122.30702
Sobol’, I. M.
3
1960
The use of Haar series in estimating the error in the computation of infinitedimensional integrals. Zbl 0189.49402
Sobol’, I. M.
3
1967
On an estimate of the accuracy of a simple multidimensional search. Zbl 0534.41013
Sobol’, I. M.
3
1982
The Monte Carlo method. 4., überarb. u. erw. Aufl. (Die Monte-Carlo-Methode. Übers. aus dem Russischen von Klaus Lommatzsch und A. Matthes.) Zbl 0719.65001
Sobol, I. M.
3
1991
Multidimensional integrals and the Monte Carlo method. Zbl 0091.14601
Sobol’, I. M.
3
1957
Experimente über die Berechnung von Integralen großer Vielfachheit. Zbl 0417.65012
Sobol’, I. M.; Levitan, Yu. L.
2
1978
On periods of pseudo-random sequences. Zbl 0275.60121
Sobol’, I. M.
2
1965
Über die Lokalisierung der charakteristischen Zahlen einer Matrix. Zbl 0297.65025
Sobol’, I. M.; Statnikov, R. B.; Ovcinnikova, N. F.
2
1973
The Monte Carlo method. (Metod Monte Karlo). 4th ed., rev. and compl. (Russian). Zbl 0573.65003
Sobol’, I. M.
2
1985
Quadrature formulae for functions of several variables satisfying a general Lipschitz condition. Zbl 0703.41029
Sobol’, I. M.
2
1989
On “freezing” of unessential variables. Zbl 0892.41015
Sobol’, I. M.
2
1996
On computational experiments in uniform distribution. Zbl 0784.11039
Sobol’, Ilya M.; Shukhman, Boris V.
2
1992
Asymmetric convergence of approximations of the Monte Carlo method. Zbl 0817.65002
Sobol’, I. M.
2
1993
An integral encountered in quadrature formulae theory. Zbl 0162.47803
Sobol’, I. M.
2
1966
Die Monte-Carlo-Methode. (The Monte Carlo method). Übersetzung aus dem Russischen von A. Matthes. Zbl 0226.65004
Sobol, I. M.
2
1971
Definition of the feasible solution set in multicriteria optimization problems with continuous, discrete, and mixed design variables. Zbl 1238.90120
Statnikov, Roman; Bordetsky, Alex; Matusov, Josef; Sobol’, Il’ya; Statnikov, Alexander
2
2009
A global search for multicriterial problems. Zbl 0770.90060
Sobol’, Ilya M.
2
1992
Über eine Verwendung ähnlicher Trajektorien in Berechnungen mit der Monte-Carlo-Methode. Zbl 0412.65003
Petrov, Yu. A.; Sobol’, I. M.
1
1979
Hypergeometrische Funktionen und gewöhnliche lineare Differentialgleichungen mit Exponentialkoeffizienten. Zbl 0415.34012
Sobol’, G. P.; Sobol’, I. M.
1
1979
Weighted quadrature formulas. Zbl 0433.41013
Sobol, I. M.
1
1979
On the distribution of random ranges. Zbl 0943.65006
Sobol, I. M.; Shukhman, B. V.; Guinzbourg, A.
1
1999
Optimization in the theory of machines by LP-search. Zbl 0258.93030
Artobolevskiĭ, I. I.; Genkin, M. D.; Grinkevich, V. K.; Sobol’, I. M.; Statnikov, R. B.
1
1971
Probability estimate of the integration error for \(\Pi_\tau\)-nets. Zbl 0295.65017
Sobol’, I. M.
1
1974
Location of the characteristic roots of a matrix. Zbl 0307.65041
Sobol’, I. M.; Statnikov, R. B.; Ovcinnikova, N. F.
1
1975
Multicriteria optimization of the mathematical models. Zbl 1075.65512
Sobol’, I. M.; Kartyshov, S. V.; Kul’chitskaya, I. A.; Levitan, Yu. L.
1
1994
Modelling correlated random variables. Zbl 1040.65003
Sobol, I. M.; Myshetskaya, E. E.
1
2003
Simulation of a class of densities. Zbl 0581.65006
Sobol’, I. M.
1
1985
Multicriteria interpretation of the regularization method for ill-posed problems. Zbl 0608.65035
Sobol’, I. M.
1
1986
On sequences of points for the evaluation of improper integrals by the quasi Monte Carlo methods. Zbl 1114.65028
Asotskii, D. I.; Sobol’, I. M.
1
2005
On the use of quasi-Monte Carlo in bootstrap estimates. Zbl 1045.62037
Sobol’, I. M.; Myshetskaya, E. E.
1
2004
Pseudo-random numbers for the machine ’Strela’. Zbl 0124.34703
Sobol’, I. M.
1
1961
The Monte Carlo method. (Метод Монте-Карло.) Zbl 0165.20401
Sobol’, I. M.
1
1968
On the solution of Peierls’ integral equation by the Monte Carlo method. Zbl 0221.65195
Sobol’, I. M.
1
1960
The Monte Carlo method. (Metod Monte-Karlo.) 2. verb. Aufl. Zbl 0235.62003
Sobol’, I. M.
1
1972
On the evaluation of infinite-dimensional integrals. Zbl 0237.65023
Sobol’, I. M.
1
1961
The Monte-Carlo method. (Metod Monte-Karlo). 3rd ed., augm. Zbl 0503.65001
Sobol’, I. M.
1
1978
Quasi-Monte Carlo method for solving Fredholm equations. Zbl 1495.65246
Sobol, I. M.; Shukhman, B. V.
1
2019
Problems with multiple objectives and ill-posed problems. Zbl 0765.90081
Sobol’, I. M.
1
1991
Untersuchung des asymptotischen Verhaltens der Lösungen einer linearen Differentialgleichung zweiter Ordnung mit Hilfe von Polarkoordinaten. Zbl 0042.32803
Sobol’, I. M.
1
1951
Quasi-Monte Carlo method for solving Fredholm equations. Zbl 1495.65246
Sobol, I. M.; Shukhman, B. V.
1
2019
On average dimensions of particle transport estimators. Zbl 1499.65007
Sobol, Ilya M.; Shukhman, Boris V.
3
2018
A limit theorem for average dimensions. Zbl 1358.11091
Shukhman, Boris V.; Sobol, Ilya M.
3
2015
Quasi-Monte Carlo: a high-dimensional experiment. Zbl 1305.11066
Sobol, Ilya M.; Shukhman, Boris V.
4
2014
A new derivative based importance criterion for groups of variables and its link with the global sensitivity indices. Zbl 1219.65005
Sobol’, I. M.; Kucherenko, S.
19
2010
Derivative based global sensitivity measures and their link with global sensitivity indices. Zbl 1167.62005
Sobol’, I. M.; Kucherenko, S.
56
2009
Definition of the feasible solution set in multicriteria optimization problems with continuous, discrete, and mixed design variables. Zbl 1238.90120
Statnikov, Roman; Bordetsky, Alex; Matusov, Josef; Sobol’, Il’ya; Statnikov, Alexander
2
2009
Monte Carlo estimators for small sensitivity indices. Zbl 1138.65004
Sobol’, I. M.; Myshetskaya, E. E.
18
2007
Erratum to: “Global sensitivity indices for the investigation of nonlinear mathematical models”. Zbl 1140.60323
Sobol’, I. M.
13
2007
On global sensitivity indices: Monte Carlo estimates affected by random errors. Zbl 1124.65004
Sobol’, Ilya M.; Shukhman, Boris V.
4
2007
On global sensitivity analysis of quasi-Monte Carlo algorithms. Zbl 1072.65004
Sobol’, I. M.; Kucherenko, S. S.
13
2005
Global sensitivity indices for the investigation of nonlinear mathematical models. Zbl 1089.26500
Sobol’, I. M.
4
2005
On sequences of points for the evaluation of improper integrals by the quasi Monte Carlo methods. Zbl 1114.65028
Asotskii, D. I.; Sobol’, I. M.
1
2005
On the use of quasi-Monte Carlo in bootstrap estimates. Zbl 1045.62037
Sobol’, I. M.; Myshetskaya, E. E.
1
2004
One more experiment on estimating high-dimensional integrals by quasi-Monte Carlo methods. Zbl 1018.65003
Sobol’, I. M.; Asotsky, D. I.
8
2003
Modelling correlated random variables. Zbl 1040.65003
Sobol, I. M.; Myshetskaya, E. E.
1
2003
Convergence estimates for crude approximations of a Pareto set. Zbl 1047.90063
Sobol’, I. M.; Myshetskaya, E. E.
4
2002
Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Zbl 1005.65004
Sobol’, I. M.
349
2001
On the use of variance reducing multipliers in Monte Carlo computations of a global sensitivity index. Zbl 1018.65002
Sobol’, I. M.; Levitan, Yu. L.
11
1999
A pseudo-random number generator for personal computers. Zbl 0949.65004
Sobol’, I. M.; Levitan, Yu. L.
6
1999
On the distribution of random ranges. Zbl 0943.65006
Sobol, I. M.; Shukhman, B. V.; Guinzbourg, A.
1
1999
Sensitivity measures, ANOVA-like techniques and the use of bootstrap. Zbl 1102.62335
Archer, G. E. B.; Saltelli, A.; Sobol, I. M.
35
1997
Error estimates for the crude approximation of the trade-off curve. Zbl 0898.90115
Sobol’, I. M.; Levitan, Yu. L.
4
1997
Quasi-Monte Carlo methods for numerical integration: Comparison of different low discrepancy sequences. Zbl 0851.65015
Radović, Igor; Sobol’, Ilya M.; Tichy, Robert F.
18
1996
A variance reducing multiplier for Monte Carlo integrations. Zbl 0858.65024
Sobol’, I. M.; Tutunnikov, A. V.
4
1996
On “freezing” of unessential variables. Zbl 0892.41015
Sobol’, I. M.
2
1996
Sensitivity analysis for nonlinear mathematical models: Numerical experiments. Zbl 0974.00507
Saltelli, A.; Sobol’, I. M.
9
1995
Integration with quasirandom sequences: Numerical experience. Zbl 0940.65502
Sobol’, Ilya M.; Shukhman, Boris V.
6
1995
A primer for the Monte Carlo method. Transl. from the Russian. Zbl 0842.65002
Sobol’, I. M.
20
1994
On the crude multidimensional search. Zbl 0823.65058
Sobol’, Ilya M.; Bakin, Sergey G.
6
1994
Multicriteria optimization of the mathematical models. Zbl 1075.65512
Sobol’, I. M.; Kartyshov, S. V.; Kul’chitskaya, I. A.; Levitan, Yu. L.
1
1994
Sensitivity estimates for nonlinear mathematical models. Zbl 1039.65505
Sobol’, I. M.
338
1993
Random and quasirandom sequences: Numerical estimates of uniformity of distribution. Zbl 0803.11042
Sobol’, I. M.; Shukman, B. V.
3
1993
Asymmetric convergence of approximations of the Monte Carlo method. Zbl 0817.65002
Sobol’, I. M.
2
1993
An efficient approach to multicriteria optimum design problems. Zbl 0749.90044
Sobol’, I. M.
9
1992
On computational experiments in uniform distribution. Zbl 0784.11039
Sobol’, Ilya M.; Shukhman, Boris V.
2
1992
A global search for multicriterial problems. Zbl 0770.90060
Sobol’, Ilya M.
2
1992
A new measure of irregularity of distribution. Zbl 0743.11039
Sobol’, Ilya M.; Nuzhdin, Oleg V.
4
1991
The Monte Carlo method. 4., überarb. u. erw. Aufl. (Die Monte-Carlo-Methode. Übers. aus dem Russischen von Klaus Lommatzsch und A. Matthes.) Zbl 0719.65001
Sobol, I. M.
3
1991
Problems with multiple objectives and ill-posed problems. Zbl 0765.90081
Sobol’, I. M.
1
1991
On sensitivity estimation for nonlinear mathematical models. Zbl 0974.00506
Sobol’, I. M.
87
1990
On a pseudo-random number generator for personal computers. Zbl 0974.65500
Levitan, Yu. L.; Sobol’, I. M.
5
1990
Quadrature formulae for functions of several variables satisfying a general Lipschitz condition. Zbl 0703.41029
Sobol’, I. M.
2
1989
On quasirandom sequences for numerical computations. Zbl 0684.65006
Levitan, Yu. L.; Markovich, N. I.; Rozin, S. G.; Sobol’, I. M.
5
1988
On quasirandom sequences for numerical computations. Zbl 0653.65007
Levitan, Yu. L.; Markovich, N. I.; Rozin, S. G.; Sobol’, I. M.
5
1988
Determination of the extremal values of a function of several variables satisfying a generalized Lipschitz condition. Zbl 0668.90070
Sobol’, I. M.
3
1988
On functions satisfying a Lipschitz condition in multidimensional problems of computational mathematics. Zbl 0641.65014
Sobol’, I. M.
3
1987
Multicriteria interpretation of the regularization method for ill-posed problems. Zbl 0608.65035
Sobol’, I. M.
1
1986
Points, uniformly filling a multidimensional cube. (Tochki, ravnomerno zapolnyayushchie mnogomernyj kub). Zbl 0564.10001
Sobol’, I. M.
4
1985
The Monte Carlo method. (Metod Monte Karlo). 4th ed., rev. and compl. (Russian). Zbl 0573.65003
Sobol’, I. M.
2
1985
Simulation of a class of densities. Zbl 0581.65006
Sobol’, I. M.
1
1985
On an estimate of the accuracy of a simple multidimensional search. Zbl 0534.41013
Sobol’, I. M.
3
1982
Selection of optimal parameters in problems with several criteria. (Vybor optimal’nykh parametrov v zadachakh so mnogimi kriteriyami). Zbl 0666.93074
Sobol’, I. M.; Statnikov, R. B.
13
1981
On the systematic search in a hypercube. Zbl 0445.65006
Sobol’, I. M.
33
1979
Über eine Verwendung ähnlicher Trajektorien in Berechnungen mit der Monte-Carlo-Methode. Zbl 0412.65003
Petrov, Yu. A.; Sobol’, I. M.
1
1979
Hypergeometrische Funktionen und gewöhnliche lineare Differentialgleichungen mit Exponentialkoeffizienten. Zbl 0415.34012
Sobol’, G. P.; Sobol’, I. M.
1
1979
Weighted quadrature formulas. Zbl 0433.41013
Sobol, I. M.
1
1979
Experimente über die Berechnung von Integralen großer Vielfachheit. Zbl 0417.65012
Sobol’, I. M.; Levitan, Yu. L.
2
1978
The Monte-Carlo method. (Metod Monte-Karlo). 3rd ed., augm. Zbl 0503.65001
Sobol’, I. M.
1
1978
Uniformly distributed sequences with an additional uniform property. Zbl 0391.10033
Sobol’, I. M.
67
1977
Uniformly distributed sequences with an additional uniform property. Zbl 0379.40003
Sobol’, I. M.
13
1976
Pseudo-random numbers for constructing discrete Markov chains by the Monte Carlo method. Zbl 0303.60059
Sobol’, I. M.
5
1975
Location of the characteristic roots of a matrix. Zbl 0307.65041
Sobol’, I. M.; Statnikov, R. B.; Ovcinnikova, N. F.
1
1975
The Monte Carlo method. Translated and adapted from the 2nd Russian edition by Robert Messer, John Stone, and Peter Fortini. Zbl 0309.65001
Sobol’, I. M.
5
1974
Probability estimate of the integration error for \(\Pi_\tau\)-nets. Zbl 0295.65017
Sobol’, I. M.
1
1974
Numerical Monte Carlo methods. (Численные методы Монте-Карло.) Zbl 0289.65001
Sobol’, I. M.
69
1973
Calculation of improper integrals using uniformly distributed sequences. Zbl 0283.41016
Sobol’, I. M.
10
1973
Über die Lokalisierung der charakteristischen Zahlen einer Matrix. Zbl 0297.65025
Sobol’, I. M.; Statnikov, R. B.; Ovcinnikova, N. F.
2
1973
The Monte Carlo method. (Metod Monte-Karlo.) 2. verb. Aufl. Zbl 0235.62003
Sobol’, I. M.
1
1972
Die Monte-Carlo-Methode. (The Monte Carlo method). Übersetzung aus dem Russischen von A. Matthes. Zbl 0226.65004
Sobol, I. M.
2
1971
Optimization in the theory of machines by LP-search. Zbl 0258.93030
Artobolevskiĭ, I. I.; Genkin, M. D.; Grinkevich, V. K.; Sobol’, I. M.; Statnikov, R. B.
1
1971
On the distribution of points in a cube and the approximate evaluation of integrals. Zbl 0185.41103
Sobol’, I. M.
228
1969
Multidimensional quadrature formulas and Haar functions. (Многомерные квадратурные формулы и функции Хаара.) Zbl 0195.16903
Sobol’, I. M.
69
1969
The Monte Carlo method. (Метод Монте-Карло.) Zbl 0165.20401
Sobol’, I. M.
1
1968
The use of Haar series in estimating the error in the computation of infinitedimensional integrals. Zbl 0189.49402
Sobol’, I. M.
3
1967
The Monte Carlo method. The method of statistical trials. Zbl 0139.35602
Busienko, N. P.; Golenko, D. I.; Shreider, Y. A.; Sobol’, I. M.; Sragovich, V. G.
17
1966
An integral encountered in quadrature formulae theory. Zbl 0162.47803
Sobol’, I. M.
2
1966
On periods of pseudo-random sequences. Zbl 0275.60121
Sobol’, I. M.
2
1965
The use of \(\omega^ 2\)-distribution for error estimation in the calculation of integrals by the Monte Carlo method. Zbl 0123.33102
Sobol’, I. M.
5
1962
The method of statistical testing (the Monte Carlo method). Edited by Yu. A. Shreĭder. (Метод статистических испытаний (Метод Монте-Карло).) Zbl 0106.32802
Buslenko, N. P.; Golenko, D. I.; Sobol’, I. M.; Sragovich, V. G.; Shreĭder, Yu. A.
4
1962
Pseudo-random numbers for the machine ’Strela’. Zbl 0124.34703
Sobol’, I. M.
1
1961
On the evaluation of infinite-dimensional integrals. Zbl 0237.65023
Sobol’, I. M.
1
1961
Accurate estimate of the error of multidimensional quadrature formulas for functions of class \(S_ p\). Zbl 0122.30702
Sobol’, I. M.
3
1960
On the solution of Peierls’ integral equation by the Monte Carlo method. Zbl 0221.65195
Sobol’, I. M.
1
1960
Multidimensional integrals and the Monte Carlo method. Zbl 0091.14601
Sobol’, I. M.
3
1957
Untersuchung des asymptotischen Verhaltens der Lösungen einer linearen Differentialgleichung zweiter Ordnung mit Hilfe von Polarkoordinaten. Zbl 0042.32803
Sobol’, I. M.
1
1951
Über das asymptotische Verhalten der Lösungen linearer Differentialgleichungen. Zbl 0038.25301
Sobol’, I. M.
4
1948
all top 5

Cited by 2,038 Authors

32 Lü, Zhenzhou
23 Dimov, Ivan Todor
21 Sobol’, Il’ya Meerovich
18 Owen, Art B.
17 Demiralp, Metin
16 Wang, Xiaoqun
14 Borgonovo, Emanuele
13 Lemieux, Christiane
13 Prieur, Clémentine
12 Gamboa, Fabrice
11 Li, Luyi
10 Alexanderian, Alen
10 Saltelli, Andrea
9 Chowdhury, Rajib
9 Congedo, Pietro Marco
9 Dick, Josef
9 Hickernell, Fred J.
9 Ökten, Giray
9 Wang, Pan
9 Wang, Xiaodi
8 Klein, Thierry E.
8 Lamboni, Matieyendou
8 L’Ecuyer, Pierre
8 Tunga, M. Alper
7 Chakraborty, Souvik
7 Iooss, Bertrand
7 Janon, Alexandre
7 Knio, Omar M.
7 Kucherenko, Sergei S.
7 Lagnoux, Agnès
7 Le Maître, Olivier P.
7 Roustant, Olivier
7 Salvetti, Maria Vittoria
7 Sloan, Ian Hugh
7 Todorov, Venelin
7 Tunga, Burcu
7 Zhou, Changcong
6 Bachoc, François
6 Faure, Henri
6 Galperin, Efim A.
6 Karniadakis, George Em
6 Leovey, Hernan
6 Niederreiter, Harald
6 Ostromsky, Tzvetan
6 Potts, Daniel
6 Rahman, Sharif
6 Sabelfeld, Karl Karlovich
6 Schmid, Wolfgang Ch.
6 Sudret, Bruno
6 Tan, Ken Seng
6 Tarantola, Stefano
5 Boyle, Phelim P.
5 Chen, Xueping
5 Cogan, Nicholas G.
5 Georgieva, Rayna
5 Hofert, Marius
5 Keller, Alexander
5 Mariotti, Alessandro
5 Mikhaĭlov, Gennadiĭ Alekseevich
5 Nair, Prasanth B.
5 Rabitz, Herschel A.
5 Raisee, Mehrdad
5 Ratto, Marco
5 Shukhman, Boris V.
5 Shyy, Wei
5 Tempone, Raúl F.
5 Zhang, Yingshan
4 Broto, Baptiste
4 Bungartz, Hans-Joachim
4 Chen, Wei
4 Cheng, Lei
4 De Lozzo, Matthias
4 Doostan, Alireza
4 Faghihi, Danial
4 Farcas, Ionut-Gabriel
4 Fathi Vajargah, Behrouz
4 Francomano, Elisa
4 Gilquin, Laurent
4 Halton, John H.
4 Hesthaven, Jan S.
4 Iaccarino, Gianluca
4 Kirillov, Kirill A.
4 Kuo, Frances Y.
4 Luo, Xiaopeng
4 Marrel, Amandine
4 Neckel, Tobias
4 Nourbakhsh, Ahmad
4 Oden, John Tinsley
4 Oladyshkin, Sergey
4 Plischke, Elmar
4 Poëtte, Gaël
4 Pulch, Roland
4 Rezaeiravesh, Saleh
4 Römisch, Werner
4 Sabino, Piergiacomo
4 Schmischke, Michael
4 Statnikov, Alexander
4 Tang, Kunkun
4 Tichy, Robert Franz
4 Wei, Pengfei
...and 1,938 more Authors
all top 5

Cited in 263 Serials

67 Computer Methods in Applied Mechanics and Engineering
53 Journal of Computational Physics
39 Applied Mathematical Modelling
35 Mathematics and Computers in Simulation
35 SIAM/ASA Journal on Uncertainty Quantification
26 Journal of Complexity
25 Computer Physics Communications
22 European Journal of Operational Research
20 Computers & Mathematics with Applications
20 Journal of Computational and Applied Mathematics
20 Monte Carlo Methods and Applications
19 Computational Geosciences
18 Communications in Statistics. Simulation and Computation
17 Journal of Mathematical Chemistry
16 Computers and Fluids
16 Journal of Statistical Computation and Simulation
14 Applied Mathematics and Computation
14 International Journal for Numerical Methods in Engineering
14 Statistics and Computing
14 Journal of Theoretical Biology
13 Mathematical and Computer Modelling
13 SIAM Journal on Scientific Computing
11 Bulletin of Mathematical Biology
10 Journal of Scientific Computing
9 Mathematical Biosciences
8 Mathematics of Computation
8 Journal of Statistical Planning and Inference
8 Computational Mechanics
8 Russian Journal of Numerical Analysis and Mathematical Modelling
8 Electronic Journal of Statistics
7 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
7 Journal of Optimization Theory and Applications
7 SIAM Journal on Numerical Analysis
7 Journal of Global Optimization
7 Computational Statistics and Data Analysis
6 Insurance Mathematics & Economics
6 Computational Optimization and Applications
6 Combustion Theory and Modelling
5 Journal of Mathematical Biology
5 Mathematica Slovaca
5 Numerische Mathematik
5 Annals of Operations Research
5 Methodology and Computing in Applied Probability
5 Quantitative Finance
5 International Journal of Computational Methods
5 Inverse Problems in Science and Engineering
4 Physica A
4 Monatshefte für Mathematik
4 Computational Mathematics and Mathematical Physics
4 Journal of Computer and Systems Sciences International
4 European Journal of Mechanics. A. Solids
4 Structural and Multidisciplinary Optimization
4 Mathematical Biosciences and Engineering
4 Engineering Optimization
4 GEM - International Journal on Geomathematics
4 Journal of Agricultural, Biological, and Environmental Statistics
3 The Annals of Statistics
3 Automatica
3 Computing
3 Fuzzy Sets and Systems
3 Journal of the American Statistical Association
3 Journal of Approximation Theory
3 Journal of Number Theory
3 Statistics & Probability Letters
3 Operations Research Letters
3 Applied Numerical Mathematics
3 International Journal of Approximate Reasoning
3 Journal of Economic Dynamics & Control
3 Numerical Algorithms
3 Mathematical Programming. Series A. Series B
3 Statistical Papers
3 Computational and Applied Mathematics
3 Applied Mathematical Finance
3 Engineering Analysis with Boundary Elements
3 Parallel Algorithms and Applications
3 Doklady Mathematics
3 European Journal of Mechanics. B. Fluids
3 Optimization and Engineering
3 Journal of Applied Mathematics
3 Comptes Rendus. Mathématique. Académie des Sciences, Paris
3 North American Actuarial Journal
3 Chebyshevskiĭ Sbornik
3 Optimization Letters
3 Journal of Statistical Theory and Practice
3 AStA. Advances in Statistical Analysis
3 The Annals of Applied Statistics
3 Journal of Computational and Graphical Statistics
3 International Journal of Systems Science. Principles and Applications of Systems and Integration
2 Biological Cybernetics
2 International Journal of Heat and Mass Transfer
2 International Journal for Numerical Methods in Fluids
2 Information Processing Letters
2 Theoretical and Mathematical Physics
2 Transport Theory and Statistical Physics
2 Information Sciences
2 Kybernetika
2 Meccanica
2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
2 Statistical Science
2 Computers & Operations Research
...and 163 more Serials
all top 5

Cited in 44 Fields

480 Numerical analysis (65-XX)
345 Statistics (62-XX)
131 Operations research, mathematical programming (90-XX)
105 Biology and other natural sciences (92-XX)
96 Probability theory and stochastic processes (60-XX)
92 Fluid mechanics (76-XX)
88 Mechanics of deformable solids (74-XX)
83 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
75 Number theory (11-XX)
72 Computer science (68-XX)
51 Approximations and expansions (41-XX)
44 Systems theory; control (93-XX)
39 Partial differential equations (35-XX)
33 Geophysics (86-XX)
26 Calculus of variations and optimal control; optimization (49-XX)
18 Ordinary differential equations (34-XX)
18 Integral equations (45-XX)
18 Statistical mechanics, structure of matter (82-XX)
15 Classical thermodynamics, heat transfer (80-XX)
14 Optics, electromagnetic theory (78-XX)
13 Harmonic analysis on Euclidean spaces (42-XX)
10 Quantum theory (81-XX)
9 Combinatorics (05-XX)
9 Dynamical systems and ergodic theory (37-XX)
9 Mechanics of particles and systems (70-XX)
8 Linear and multilinear algebra; matrix theory (15-XX)
8 Functional analysis (46-XX)
5 Convex and discrete geometry (52-XX)
5 Information and communication theory, circuits (94-XX)
4 Measure and integration (28-XX)
3 Real functions (26-XX)
2 General and overarching topics; collections (00-XX)
2 Geometry (51-XX)
1 History and biography (01-XX)
1 Mathematical logic and foundations (03-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Associative rings and algebras (16-XX)
1 Group theory and generalizations (20-XX)
1 Special functions (33-XX)
1 Integral transforms, operational calculus (44-XX)
1 Operator theory (47-XX)
1 General topology (54-XX)
1 Algebraic topology (55-XX)
1 Astronomy and astrophysics (85-XX)

Citations by Year

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