Bairstow method (for zeros of polynomials)
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21—30 of 417 matching pages
21: Bibliography R
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Methods of Modern Mathematical Physics, Vol. 2, Fourier Analysis, Self-Adjointness.
Academic Press, New York.
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Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators.
Academic Press, New York.
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Methods of Modern Mathematical Physics, Vol. 3, Scattering Theory.
Academic Press, New York.
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Erratum to:Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging.
Computing in Science and Engineering 23 (4), pp. 91.
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Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging.
Computing in Science and Engineering 23 (3), pp. 56–64.
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22: 27.18 Methods of Computation: Primes
§27.18 Methods of Computation: Primes
►An overview of methods for precise counting of the number of primes not exceeding an arbitrary integer is given in Crandall and Pomerance (2005, §3.7). … Oliveira e Silva has calculated for , using the combinatorial methods of Lagarias et al. (1985) and Deléglise and Rivat (1996); see Oliveira e Silva (2006). … ►The AKS (Agrawal–Kayal–Saxena) algorithm is the first deterministic, polynomial-time, primality test. …23: Bibliography G
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New inequalities for the zeros of Jacobi polynomials.
SIAM J. Math. Anal. 18 (6), pp. 1549–1562.
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Asymptotics and bounds for the zeros of Laguerre polynomials: A survey.
J. Comput. Appl. Math. 144 (1-2), pp. 7–27.
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On mean convergence of extended Lagrange interpolation.
J. Comput. Appl. Math. 43 (1-2), pp. 19–35.
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A method for evaluating certain Bessel integrals.
Z. Angew. Math. Phys. 30 (4), pp. 722–723.
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Method for evaluation of zeros of Bessel functions.
J. Inst. Math. Appl. 11, pp. 57–72.
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24: 3.5 Quadrature
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►Stroud and Secrest (1966) includes computational methods and extensive tables.
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►The are the monic Hermite polynomials
(§18.3).
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►Further methods are given in Clendenin (1966) and Lyness (1985).
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►For integrals in higher dimensions, Monte Carlo methods are another—often the only—alternative.
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25: 34.9 Graphical Method
§34.9 Graphical Method
►The graphical method establishes a one-to-one correspondence between an analytic expression and a diagram by assigning a graphical symbol to each function and operation of the analytic expression. …For an account of this method see Brink and Satchler (1993, Chapter VII). For specific examples of the graphical method of representing sums involving the , and symbols, see Varshalovich et al. (1988, Chapters 11, 12) and Lehman and O’Connell (1973, §3.3).26: 24.19 Methods of Computation
§24.19 Methods of Computation
… ►For higher values of more efficient methods are available. …A similar method can be used for the Euler numbers based on (4.19.5). … ►Another method is based on the identities … ►We list here three methods, arranged in increasing order of efficiency. …27: Peter A. Clarkson
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►He is a member of the editorial boards of nine international journals and has served as Chair, Vice-Chair, and Secretary of the SIAM Activity Group on Orthogonal Polynomials and Special Functions.
►Clarkson has published numerous papers on integrable systems (primarily Painlevé equations), special functions, and symmetry methods for differential equations.
… Kruskal, he developed the “direct method” for determining symmetry solutions of partial differential equations in New similarity reductions of the Boussinesq equation (with M.
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28: Bibliography P
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Exactification of the method of steepest descents: The Bessel functions of large order and argument.
Proc. Roy. Soc. London Ser. A 460, pp. 2737–2759.
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Evaluation of Fermi-Dirac Integral.
In Nonlinear Numerical Methods and Rational Approximation
(Wilrijk, 1987), A. Cuyt (Ed.),
Mathematics and Its Applications, Vol. 43, pp. 435–444.
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Modified Clenshaw-Curtis method for the computation of Bessel function integrals.
BIT 23 (3), pp. 370–381.
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A survey of numerical methods for the computation of Bessel function integrals.
Rend. Sem. Mat. Univ. Politec. Torino (Special Issue), pp. 249–265.
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A method for computing Bessel function integrals.
J. Comput. Phys. 75 (2), pp. 334–344.
29: 33.23 Methods of Computation
§33.23 Methods of Computation
►§33.23(i) Methods for the Confluent Hypergeometric Functions
►The methods used for computing the Coulomb functions described below are similar to those in §13.29. … ►§33.23(vi) Other Numerical Methods
►Curtis (1964a, §10) describes the use of series, radial integration, and other methods to generate the tables listed in §33.24. …30: Bibliography B
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Asymptotic methods in enumeration.
SIAM Rev. 16 (4), pp. 485–515.
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Numerical Methods for Least Squares Problems.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
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Uniform asymptotic expansion of Charlier polynomials.
Methods Appl. Anal. 1 (3), pp. 294–313.
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Asymptotic behavior of the Pollaczek polynomials and their zeros.
Stud. Appl. Math. 96, pp. 307–338.
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Approximations for the late coefficients in asymptotic expansions arising in the method of steepest descents.
Methods Appl. Anal. 2 (4), pp. 475–489.
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