numerical%20inversion
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10 matching pages
1: 18.40 Methods of Computation
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§18.40(ii) The Classical Moment Problem
… ►Stieltjes Inversion via (approximate) Analytic Continuation
… ►Results of low ( to decimal digits) precision for are easily obtained for to . … ►Histogram Approach
… ►Derivative Rule Approach
…2: Bibliography C
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The inverse of the error function.
Pacific J. Math. 13 (2), pp. 459–470.
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Numerical computation of real or complex elliptic integrals.
Numer. Algorithms 10 (1-2), pp. 13–26.
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Power series for inverse Jacobian elliptic functions.
Math. Comp. 77 (263), pp. 1615–1621.
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A method for numerical calculation of Fourier integrals.
Numer. Math. 8 (5), pp. 422–436.
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A method for numerical integration on an automatic copmputer.
Numer. Math. 2 (4), pp. 197–205.
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3: Bibliography I
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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Centre for Experimental and Constructive Mathematics, Simon Fraser University, Canada.
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Highly Oscillatory Quadrature: The Story So Far.
In Numerical Mathematics and Advanced Applications, A. Bermudez de Castro and others (Eds.),
pp. 97–118.
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A First Course in the Numerical Analysis of Differential Equations.
Cambridge Texts in Applied Mathematics, No. 15, Cambridge University Press, Cambridge.
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More on electrostatic models for zeros of orthogonal polynomials.
Numer. Funct. Anal. Optim. 21 (1-2), pp. 191–204.
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4: Bibliography K
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Numerical Methods and Software.
Prentice Hall, Englewood Cliffs, N.J..
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The second Painlevé equation in electric probe theory. Some numerical solutions.
Zh. Vychisl. Mat. Mat. Fiz. 38 (6), pp. 992–1000 (Russian).
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The second Painlevé equation in the electrostatic probe theory: Numerical solutions for the partial absorption of charged particles by the surface.
Technical Physics 49 (1), pp. 1–7.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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On Nielsen’s generalized polylogarithms and their numerical calculation.
Nordisk Tidskr. Informationsbehandling (BIT) 10, pp. 38–73.
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5: Bibliography S
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Orthogonal polynomials arising in the numerical evaluation of inverse Laplace transforms.
Math. Tables Aids Comput. 9 (52), pp. 164–177.
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Numerical evaluation of the Hankel transform.
Comput. Phys. Comm. 116 (2-3), pp. 278–294.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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On numerical Bessel transformation.
Comput. Phys. Comm. 16 (3), pp. 383–387.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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6: 12.11 Zeros
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►Numerical calculations in this case show that corresponds to the th zero on the string; compare §7.13(ii).
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►where is the function inverse to , defined by (12.10.39) (see also (12.10.41)), and
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12.11.9
►where the numerical coefficients have been rounded off.
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7: Bibliography O
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On the asymptotic and numerical solution of linear ordinary differential equations.
SIAM Rev. 40 (3), pp. 463–495.
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Numerical solution of second-order linear difference equations.
J. Res. Nat. Bur. Standards Sect. B 71B, pp. 111–129.
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Numerical solution of Riemann-Hilbert problems: Painlevé II.
Found. Comput. Math. 11 (2), pp. 153–179.
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Numerical evaluation of the dilogarithm of complex argument.
Celestial Mech. Dynam. Astronom. 62 (1), pp. 93–98.
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Numerical Computing with IEEE Floating Point Arithmetic.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
8: Bibliography R
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Rational Chebyshev approximation by Remes’ algorithms.
Numer. Math. 7 (4), pp. 322–330.
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On the definition and properties of generalized - symbols.
J. Math. Phys. 20 (12), pp. 2398–2415.
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Universality properties of Gaussian quadrature, the derivative rule, and a novel approach to Stieltjes inversion.
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Elliptic Integrals of the First and Second Kind – Comparison of Bulirsch’s and Carlson’s Algorithms for Numerical Calculation.
In Special Functions (Hong Kong, 1999), C. Dunkl, M. Ismail, and R. Wong (Eds.),
pp. 293–308.
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Computation of Hankel (Bessel) functions of complex index and argument by numerical integration of a Schläfli contour integral.
Ž. Vyčisl. Mat. i Mat. Fiz. 13, pp. 1415–1424, 1636.
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9: 19.36 Methods of Computation
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►Numerical differences between the variables of a symmetric integral can be reduced in magnitude by successive factors of 4 by repeated applications of the duplication theorem, as shown by (19.26.18).
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19.36.11
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►The cases and require different treatment for numerical purposes, and again precautions are needed to avoid cancellations.
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►For computation of Legendre’s integral of the third kind, see Abramowitz and Stegun (1964, §§17.7 and 17.8, Examples 15, 17, 19, and 20).
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►Numerical quadrature is slower than most methods for the standard integrals but can be useful for elliptic integrals that have complicated representations in terms of standard integrals.
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10: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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Numerical calculation of a generalized complete elliptic integral.
Rev. Mod. Phys. 10, pp. 264–269.
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Numerical Methods for Least Squares Problems.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
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Numerical evaluation of continued fractions.
SIAM Rev. 6 (4), pp. 383–421.
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Numerical aspects of Mathieu eigenvalues.
Rend. Circ. Mat. Palermo (2) 15, pp. 51–97.
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