Edit Profile (opens in new tab) Sobol’, Il’ya Meerovich Co-Author Distance Author ID: sobol.ilya-m Published as: Sobol’, I. M.; Sobol, I. M.; Sobol’, Ilya M.; Sobol, Ilya M.; Sobol’, Il’ya more...less 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 Co-Authors 67 single-authored 10 Shukhman, Boris V. 8 Levitan, Yu. L. 7 Myshetskaya, E. E. 6 Statnikov, R. B. 3 Asotsky, D. I. 3 Kucherenko, Sergei S. 2 Artobolevskii, I. I. 2 Golenko, Dmitri I. 2 Markovich, N. I. 2 Ovcinnikova, N. F. 2 Petrov, Yu. A. 2 Rozin, S. G. 2 Saltelli, Andrea 2 Shreider, Yu. A. 2 Sobol’, G. P. 2 Sragovich, Vladimir G. 1 Archer, G. E. B. 1 Bakin, Sergey G. 1 Bordetsky, Alex 1 Busienko, N. P. 1 Buslenko, Nikolai Pantelejmonovich 1 Chetverushkin, Boris Nikolaevich 1 Genkin, M. D. 1 German, V. A. 1 Gol’din, Vladimir Ya. 1 Gorbacheva, N. B. 1 Grinkevich, V. K. 1 Kalitkin, Nikolaĭ Nikolaevich 1 Kartyshov, Sergey V. 1 Kul’chitskaya, I. A. 1 Matusov, Josef 1 Messer, Robert 1 Nuzhdin, Oleg V. 1 Radović, Igor 1 Samarskiĭ, Aleksandr Andreevich 1 Sergeev, V. I. 1 Shukman, B. V. 1 Statnikov, Alexander 1 Statnikov, I. N. 1 Statnikov, Roman 1 Tichy, Robert Franz 1 Tishkin, Vladimir Fëdorovich 1 Trikuzov, A. I. 1 Tutunnikov, A. V. 1 Vladimirov, Vasiliĭ Sergeevich 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 all top 5 Fields 74 Numerical analysis (65-XX) 14 Number theory (11-XX) 13 Statistics (62-XX) 13 Operations research, mathematical programming (90-XX) 11 Approximations and expansions (41-XX) 8 Probability theory and stochastic processes (60-XX) 6 Systems theory; control (93-XX) 3 Ordinary differential equations (34-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 General and overarching topics; collections (00-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Real functions (26-XX) 2 Sequences, series, summability (40-XX) 2 Operator theory (47-XX) 1 History and biography (01-XX) 1 Special functions (33-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications 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 cited Publications top 5 cited Publications 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 Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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