MONTE CARLO METHODS FOR SOLVING MULTIVARIABLE PROBLEMS

This paper opens with a brief general introduction on the nature of Monte Carlo methods that can be skipped by readers acquainted with them. I then deal more specifically with the application of these methods to multivariable problems, and I indicate certain relatively unexplored areas of this field where further research might be profitable. As I believe is appropriate, some of my material is exploratory, speculative, and controversial, and accordingly I hope it will stimulate discussion.

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  J. G. Corput.  Diophantische Ungleichungen. I. Zur Gleichverteilung Modulo Eins , 1931 .

[3]  J. I.  The Design of Experiments , 1936, Nature.

[4]  K. Mahler.  On the fractional parts of the powers of a rational number , 1939 .

[5]  A. N. Lowan,et al.  Tables of lagrangian interpolation coefficients , 1944 .

[6]  Sequences of points on a circle , 1949 .

[7]  O. Kempthorne.  The Design and Analysis of Experiments , 1952 .

[8]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[9]  K. F. Roth.  On irregularities of distribution , 1954 .

[10]  J. Hammersley,et al.  Poor Man's Monte Carlo , 1954 .

[11]  H. Kahn.  APPLICATIONS OF MONTE CARLO , 1954 .

[12]  O. Taussky,et al.  Generation and testing of pseudo-random numbers , 1954 .

[13]  I NICOLETTI,et al.  The Planning of Experiments , 1936, Rivista di clinica pediatrica.

[14]  J. Hammersley,et al.  A new Monte Carlo technique: antithetic variates , 1956, Mathematical Proceedings of the Cambridge Philosophical Society.

[15]  J. M. Hammersley,et al.  Conditional Monte Carlo , 1956, JACM.

[16]  J. G. Mauldon,et al.  General principles of antithetic variates , 1956, Mathematical Proceedings of the Cambridge Philosophical Society.

[17]  Subdivision of an interval by a sequence of points , 1957 .

[18]  K. Mahler.  On the fractional parts of the powers of a rational number (II) , 1957 .

[19]  Eine Verschärfung des Schubfächerprinzips in einem linearen Intervall , 1957 .

[20]  J. G. Wendel.  Groups and Conditional Monte Carlo , 1957 .

[21]  Zum Schubfächerprinzip im linearen Intervall , 1957 .

[22]  D. C. Handscomb,et al.  A Method for Increasing the Efficiency of Monte Carlo Integration , 1957, JACM.

[23]  John W. Tukey,et al.  Antithesis or regression? , 1957, Mathematical Proceedings of the Cambridge Philosophical Society.

[24]  K. W. Morton.  A Generalisation of the Antithetic Variate Technique for Evaluating Integrals , 1957 .

[25]  D. Ridout.  Rational approximations to algebraic numbers , 1957 .

[26]  W. Coles.  On a theorem of van der Corput on uniform distribution , 1957, Mathematical Proceedings of the Cambridge Philosophical Society.

[27]  Walter L. Smith.  Renewal Theory and its Ramifications , 1958 .

[28]  J. M. Hammersley,et al.  Proof of the antithetic variates theorem for n > 2 , 1958 .

[29]  J. Beardwood,et al.  The shortest path through many points , 1959, Mathematical Proceedings of the Cambridge Philosophical Society.

[30]  C. D. Allen.  A Method for the Reduction of Empirical Multi-Variable Functions , 1959, Comput. J..