Pdf J.h.wilkinson C.reinsch Handbook For Automatic Computation Pdf

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Chebyshev expansions for the error and related functions

Full-text PDF Free Access. Handbook for automatic computation. II, Springer-Verlag, New York-Heidelberg, 1971. Linear algebra; Compiled by J. Advancing research. Creating connections. Algorithms for triangular decomposition of block Hankel and Toeplitz matrices with application to factoring positive matrix polynomials. Bibliography for James Hardy Wilkinson, 1919 – 1986 June 11, 2019 Additions, errors and corrections to sven.hammarling@btinternet.com please. Much of this is derived.


Author:J. L. Schonfelder
Journal:Math. Comp. 32 (1978), 1232-1240
MSC:Primary 65D20; Secondary 33A20
DOI:https://doi.org/10.1090/S0025-5718-1978-0494846-8
MathSciNet review:0494846
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Pdf J.h.wilkinson C.reinsch Handbook For Automatic Computation Pdf File

Abstract: New 30 decimal place Chebyshev expansions, which can be used to obtain approximations up to that accuracy, for the error function and its complement are presented. Bilinear and biquadratic mappings of the independent variable have been employed, in one case to improve convergence and in the other to increase the basic approximation range. The practical effects of these mappings are discussed, and the method used to generate the tabulated expansions is outlined. The expansions here presented form the basis of the routines in the S15 chapter of the NAG library.

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[2]
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[Y]
L. LUKE, Mathematical Functions and their Approximations, Academic Press, New York, 1976, pp. 123-124. MR 0501762 (58:19039)
[Y]
L. LUKE, Algorithms for the Computation of Mathematical Functions, Academic Press, New York, 1978. MR 0494840 (58:13624)
[3]
G. F. MILLER, Private communication.
[4]
J. L. SCHONFELDER, 'The NAG library and its special functions chapter,' International Computing Symposium 1974 (A. Günther et al., Editors), North-Holland, Amsterdam; American Elsevier, New York, 1974.
[J]
L. SCHONFELDER, 'Special functions in the NAG library,' Software for Numerical Mathematics (D. J. Evans, Editor), (Proc. Conf., 1973), Academic Press, London and New York, 1974, pp. 285-300.
[J]
L. SCHONFELDER, 'The production of special function routines for a multi-machine library,' Software-Practice and Experience, vol. 6, 1976, pp. 71-82.
[5]
L. FOX & I. B. PARKER, Chebyshev Polynomials in Numerical Analysis, Oxford Univ. Press, London and New York, 1968. MR 0228149 (37:3733)
[6]
J. L. SCHONFELDER, 'Generation of high precision Chebyshev expansions.' (Manuscript in preparation.)
[7]
J. H. WILKINSON & C. REINSCH, Linear Algebra, Handbook for Automatic Computation, Vol. 2 (Grundlehren der math. Wissenschaften, Band 186, vol. 2), Springer-Verlag, Berlin and New York, 1971. MR 0461856 (57:1840)
[8]
J. L. SCHONFELDER & J. T. THOMASON, 'Applications support by direct language extension--An arbitrary precision arithmetic facility in Algol 68,' International Computing Symposium 1975 (Proc. Sympos., Antibes, 1975), E. Gelenbe and D. Potier (Editors), North-Holland, Amsterdam; American Elsevier, New York, 1975.

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Additional Information
DOI:https://doi.org/10.1090/S0025-5718-1978-0494846-8
Keywords:Special function approximation,error functions,Chebyshev expansions
Article copyright:© Copyright 1978American Mathematical Society