Monte-Carlo methods

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31: Alexander A. Its

… ►Books by Its are The Isomonodromic Deformation Method in the Theory of Painlevé Equations (with V. …

32: Vadim B. Kuznetsov

… ►Kuznetsov published papers on special functions and orthogonal polynomials, the quantum scattering method, integrable discrete many-body systems, separation of variables, Bäcklund transformation techniques, and integrability in classical and quantum mechanics. …

33: 21.10 Methods of Computation

§21.10 Methods of Computation

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34: 27.20 Methods of Computation: Other Number-Theoretic Functions

§27.20 Methods of Computation: Other Number-Theoretic Functions

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35: 27.22 Software

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Mathematica. PrimeQ combines strong pseudoprime tests for the bases 2 and 3 and a Lucas pseudoprime test. No known composite numbers pass these three tests, and Bleichenbacher (1996) has shown that this combination of tests proves primality for integers below ${10}^{16}$. Provable PrimeQ uses the Atkin–Goldwasser–Kilian–Morain Elliptic Curve Method to prove primality. FactorInteger tries Brent–Pollard rho, Pollard $p-1$, and then cfrac after trial division. See §27.19. ecm is available also, and the Multiple Polynomial Quadratic sieve is expected in a future release.

For additional Mathematica routines for factorization and primality testing, including several different pseudoprime tests, see Bressoud and Wagon (2000).

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ECMNET Project. Links to software for elliptic curve methods of factorization and primality testing.

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36: Daniel W. Lozier

… ►Then he transferred to NIST (then known as the National Bureau of Standards), where he collaborated for several years with the Building and Fire Research Laboratory developing and applying finite-difference and spectral methods to differential equation models of fire growth. … ►In 2008 he was named an Honorary Fellow of the European Society of Computational Methods in Sciences and Engineering, and in 2017 was named a Fellow of the Washington Academy of Sciences.

37: 3.7 Ordinary Differential Equations

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§3.7(ii) Taylor-Series Method: Initial-Value Problems

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§3.7(iii) Taylor-Series Method: Boundary-Value Problems

… ►General methods for boundary-value problems for ordinary differential equations are given in Ascher et al. (1995). … ►For further information, including other methods and examples, see Pryce (1993, §2.5.1). ►

§3.7(v) Runge–Kutta Method

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38: Bibliography I

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The factorization method. Rev. Modern Phys. 23 (1), pp. 21–68.

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Referenced by:

§18.38(iii).

Encodings:

BibTeX

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The $J$-matrix method. Adv. in Appl. Math. 46 (1-4), pp. 379–395.

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External Links:

ISSN 0196-8858, Document, Link, MathReview (Boris Petrovich Osilenker)

Referenced by:

§18.39(iv).

Encodings:

BibTeX

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On the asymptotic analysis of the Painlevé equations via the isomonodromy method. Nonlinearity 7 (5), pp. 1291–1325.

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External Links:

ISSN 0951-7715, Document, MathReview (Alexander Vladimirovich Kitaev), ZentralBlatt

Referenced by:

§32.11(iii).

Encodings:

BibTeX

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The Isomonodromic Deformation Method in the Theory of Painlevé Equations. Lecture Notes in Mathematics, Vol. 1191, Springer-Verlag, Berlin.

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External Links:

ISBN 3-540-16483-9, MathReview (Alexander A. Pankov), ZentralBlatt

Referenced by:

§32.11(iv), §32.4(i), Profile Alexander A. Its.

Encodings:

BibTeX

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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.

Encodings:

BibTeX

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39: 1.15 Summability Methods

§1.15 Summability Methods

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Abel Summability

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Cesàro Summability

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§1.15(ii) Regularity

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40: 36.15 Methods of Computation

§36.15 Methods of Computation

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