Monte Carlo methods

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1: 27.19 Methods of Computation: Factorization

… ►Type I probabilistic algorithms include the Brent–Pollard rho algorithm (also called Monte Carlo method), the Pollard $p-1$ algorithm, and the Elliptic Curve Method (ecm). …

2: Bibliography I

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Statistical Field Theory: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. Vol. 2, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-37012-4; 0-521-40806-7, MathReview (C. A. Hurst), ZentralBlatt

Referenced by:

2nd item.

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BibTeX

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3: 3.5 Quadrature

§3.5 Quadrature

… ►For integrals in higher dimensions, Monte Carlo methods are another—often the only—alternative. The standard Monte Carlo method samples points uniformly from the integration region to estimate the integral and its error. …With $N$ function values, the Monte Carlo method aims at an error of order $1/\sqrt{N}$, independently of the dimension of the domain of integration. …

4: Bibliography S

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Adaptive Quasi-Monte Carlo Integration Based on MISER and VEGAS. In Monte Carlo and Quasi-Monte Carlo Methods 2002, pp. 393–406.

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External Links:

MathReview Entry, ZentralBlatt

Referenced by:

§3.5(x).

Encodings:

BibTeX

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5: 35.10 Methods of Computation

§35.10 Methods of Computation

… ►Other methods include numerical quadrature applied to double and multiple integral representations. See Yan (1992) for the ${}_1{}^{}F_1^{}$ and ${}_2{}^{}F_1^{}$ functions of matrix argument in the case $m=2$, and Bingham et al. (1992) for Monte Carlo simulation on $𝐎(m)$ applied to a generalization of the integral (35.5.8). …