quotient-difference algorithm

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1: 3.10 Continued Fractions

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Quotient-Difference Algorithm

… ► … ►We continue by means of the rhombus rule … ►The quotient-difference algorithm is frequently unstable and may require high-precision arithmetic or exact arithmetic. … …

2: Bibliography S

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The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions. 2nd edition, Graduate Texts in Mathematics, Vol. 203, Springer-Verlag, New York.

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Notes:

First edition published by Wadsworth & Brooks/Cole Advanced Books & Software, 1991.

External Links:

ISBN 0-387-95067-2, MathReview, ZentralBlatt

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§26.19.

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BibTeX

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Algorithm AS 239. Chi-squared and incomplete gamma integral. Appl. Statist. 37 (3), pp. 466–473.

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Notes:

Double-precision Fortran.

External Links:

FullText, Code

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5th item.

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BibTeX

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Matrix Algorithms. Vol. 2: Eigensystems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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External Links:

ISBN 0-89871-503-2, MathReview Entry, ZentralBlatt

Referenced by:

§3.2(vi).

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BibTeX

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A stable quotient-difference algorithm. Math. Comp. 34 (150), pp. 515–519.

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External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

§3.10(ii).

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BibTeX

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Department of Computer Science, Stony Brook University, New York.

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Notes:

A collection of over 70 combinatorial algorithms.

External Links:

Stony Brook Algorithm Repository

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7th item.

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3: 27.19 Methods of Computation: Factorization

… ►Deterministic algorithms are slow but are guaranteed to find the factorization within a known period of time. …Fermat’s algorithm is another; see Bressoud (1989, §5.1). ►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). Descriptions of these algorithms are given in Crandall and Pomerance (2005, §§5.2, 5.4, and 7.4). … ►These algorithms include the Continued Fraction Algorithm (cfrac), the Multiple Polynomial Quadratic Sieve (mpqs), the General Number Field Sieve (gnfs), and the Special Number Field Sieve (snfs). …

4: 35.12 Software

… ►In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. … ►For an algorithm to evaluate zonal polynomials, and an implementation of the algorithm in Maple by Zeilberger, see Lapointe and Vinet (1996).

5: 17.19 Software

… ►In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. …

6: 26.22 Software

… ►In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. … ►

Stony Brook Algorithm Repository (website).

… ►For algorithms for counting and analyzing combinatorial structures see Knuth (1993), Nijenhuis and Wilf (1975), and Stanton and White (1986).

7: 27.18 Methods of Computation: Primes

… ►Two simple algorithms for proving primality require a knowledge of all or part of the factorization of $n-1,n+1$, or both; see Crandall and Pomerance (2005, §§4.1–4.2). These algorithms are used for testing primality of Mersenne numbers, $2^n-1$, and Fermat numbers, $2^{2^n}+1$. … ►The APR (Adleman–Pomerance–Rumely) algorithm for primality testing is based on Jacobi sums. … ►The AKS (Agrawal–Kayal–Saxena) algorithm is the first deterministic, polynomial-time, primality test. … ►The ECPP (Elliptic Curve Primality Proving) algorithm handles primes with over 20,000 digits. …

8: 21.11 Software

… ►In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. …

9: 35.10 Methods of Computation

… ►Koev and Edelman (2006) utilizes combinatorial identities for the zonal polynomials to develop computational algorithms for approximating the series expansion (35.8.1). These algorithms are extremely efficient, converge rapidly even for large values of $m$, and have complexity linear in $m$.

10: 18.42 Software

… ►In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. …