Bairstow method (for zeros of polynomials)

SearchAdvancedHelp

(0.003 seconds)

11—20 of 417 matching pages

11: 28.34 Methods of Computation

§28.34 Methods of Computation

… ►Methods available for computing the values of $w_{\text{I}}(\pi ;a,\pm q)$ needed in (28.2.16) include: … ►

Methods described in §3.7(iv) applied to the differential equation (28.2.1) with the conditions (28.2.5) and (28.2.16).

… ►

Asymptotic approximations by zeros of orthogonal polynomials of increasing degree. See Volkmer (2008). This method also applies to eigenvalues of the Whittaker–Hill equation (§28.31(i)) and eigenvalues of Lamé functions (§29.3(i)).

… ►

Solution of (28.2.1) by boundary-value methods; see §3.7(iii). This can be combined with §28.34(ii)(c).

…

12: Bibliography K

… ►

Numerical Methods and Software. Prentice Hall, Englewood Cliffs, N.J..

ⓘ

Notes:

Includes collection of single- and double-precision Fortran subroutines.

External Links:

ISBN 0-13-627258-4, GAMS (package NMS), ZentralBlatt

Referenced by:

NMS (free collection of Fortran subroutines).

Encodings:

BibTeX

… ►

Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

ⓘ

External Links:

Document, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.18(i).

Encodings:

BibTeX

►

The Rayleigh function: Theory and computational methods. Zh. Vychisl. Mat. Mat. Fiz. 39 (12), pp. 1962–2006.

ⓘ

Notes:

Translation in Comput. Math. Math. Phys. 39 (1999), No. 12, pp. 1883–1925.

External Links:

ISSN 0044-4669, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.21(xiii).

Encodings:

BibTeX

… ►

An indirect method for evaluating certain infinite integrals. Z. Angew. Math. Phys. 29 (3), pp. 380–386.

ⓘ

External Links:

ISSN 0044-2275, Document, MathReview, ZentralBlatt

Referenced by:

§10.71(ii).

Encodings:

BibTeX

… ►

Zeros of exceptional Hermite polynomials. J. Approx. Theory 200, pp. 28–39.

ⓘ

External Links:

ISSN 0021-9045, Document, Link, MathReview (Mario Pérez Riera)

Referenced by:

§18.39(i).

Encodings:

BibTeX

…

13: 18.38 Mathematical Applications

… ►

Differential Equations: Spectral Methods

►Linear ordinary differential equations can be solved directly in series of Chebyshev polynomials (or other OP’s) by a method originated by Clenshaw (1957). This process has been generalized to spectral methods for solving partial differential equations. … ►

Quadrature “Extended” to Pseudo-Spectral (DVR) Representations of Operators in One and Many Dimensions

… ►These methods have become known as pseudo-spectral, and are overviewed in Cerjan (1993), and Shizgal (2015). …

14: 35.10 Methods of Computation

§35.10 Methods of Computation

►For small values of $\Vert 𝐓\Vert$ the zonal polynomial expansion given by (35.8.1) can be summed numerically. … ►Other methods include numerical quadrature applied to double and multiple integral representations. … ►Koev and Edelman (2006) utilizes combinatorial identities for the zonal polynomials to develop computational algorithms for approximating the series expansion (35.8.1). …

15: 1 Algebraic and Analytic Methods

Chapter 1 Algebraic and Analytic Methods

…

16: 27.19 Methods of Computation: Factorization

§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). …As of January 2009 the largest prime factors found by these methods are a 19-digit prime for Brent–Pollard rho, a 58-digit prime for Pollard $p-1$, and a 67-digit prime for ecm. … ►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). …

17: 29 Lamé Functions

…

18: Bibliography L

… ►

The real zeros of the Bernoulli polynomials. J. Approx. Theory 58 (2), pp. 124–150.

ⓘ

External Links:

ISSN 0021-9045, Document, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§24.12(i), §24.9.

Encodings:

BibTeX

… ►

An application of the finite element approximation method to find the complex zeros of the modified Bessel function $K_n(z)$ . Math. Comp. 33 (148), pp. 1299–1306.

ⓘ

External Links:

ISSN 0025-5718, FullText, MathReview (R. P. Boas, Jr.), ZentralBlatt

Referenced by:

§10.74(vi), 2nd item.

Encodings:

BibTeX

… ►

Approximation of orthogonal polynomials in terms of Hermite polynomials. Methods Appl. Anal. 6 (2), pp. 131–146.

ⓘ

External Links:

ISSN 1073-2772, Pdf, MathReview, ZentralBlatt

Referenced by:

§18.15(vi), §18.16(vi).

Encodings:

BibTeX

… ►

Monotonicity of the zeros of the third derivative of Bessel functions. Methods Appl. Anal. 2 (1), pp. 103–111.

ⓘ

External Links:

ISSN 1073-2772, FullText, MathReview (N. Hayek Calil), ZentralBlatt

Referenced by:

§10.21(iv).

Encodings:

BibTeX

… ►

The zeros of the third derivative of Bessel functions of order less than one. Methods Appl. Anal. 2 (2), pp. 147–159.

ⓘ

External Links:

ISSN 1073-2772, FullText, MathReview (Evangelos Ifantis), ZentralBlatt

Referenced by:

§10.21(iv), §10.21(iv).

Encodings:

BibTeX

…

19: Bibliography D

… ►

On the zeros of generalized Bessel polynomials. I. Nederl. Akad. Wetensch. Indag. Math. 84 (1), pp. 1–13.

ⓘ

External Links:

ISSN 0019-3577, Document, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§10.49(ii), §10.58.

Encodings:

BibTeX

►

On the zeros of generalized Bessel polynomials. II. Nederl. Akad. Wetensch. Indag. Math. 84 (1), pp. 14–25.

ⓘ

External Links:

ISSN 0019-3577, Document, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§10.49(ii), §10.58.

Encodings:

BibTeX

… ►

Zeros of Bernoulli, generalized Bernoulli and Euler polynomials. Mem. Amer. Math. Soc. 73 (386), pp. iv+94.

ⓘ

External Links:

ISSN 0065-9266, MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.12(i), §24.12(iii), §24.16(ii).

Encodings:

BibTeX

… ►

On multiple zeros of Bernoulli polynomials. Acta Arith. 134 (2), pp. 149–155.

ⓘ

External Links:

ISSN 0065-1036, Document, MathReview (Arnold M. Adelberg), ZentralBlatt

Referenced by:

§24.12(iv).

Encodings:

BibTeX

… ►

Asymptotic approximations for the Jacobi and ultraspherical polynomials, and related functions. Methods Appl. Anal. 6 (3), pp. 21–56.

ⓘ

External Links:

ISSN 1073-2772, Pdf, MathReview (Walter Van Assche), ZentralBlatt

Referenced by:

§15.12(iii), §18.15(i), §18.15(vi).

Encodings:

BibTeX

…

20: 25.18 Methods of Computation

§25.18 Methods of Computation

►

§25.18(i) Function Values and Derivatives

… ►

§25.18(ii) Zeros

►Most numerical calculations of the Riemann zeta function are concerned with locating zeros of $\zeta \left(\frac{1}{2}+\mathrm{i}t\right)$ in an effort to prove or disprove the Riemann hypothesis, which states that all nontrivial zeros of $\zeta \left(s\right)$ lie on the critical line $\mathrm{\Re }s=\frac{1}{2}$. Calculations to date (2008) have found no nontrivial zeros off the critical line. …