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

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

Full-text PDF Free Access. Abstract References. Handbook for automatic computation. II, Springer-Verlag, New York-Heidelberg, 1971. Linear algebra; Compiled by J. Wilkinson and C. Reinsch; Die Grundlehren der Mathematischen Wissenschaften, Band 186. Description: This journal, begun in 1943 as Mathematical Tables and Other Aids to Computation, publishes original articles on all aspects of numerical mathematics, book reviews, mathematical tables, and technical notes.It is devoted to advances in numerical analysis, the application of computational methods, high speed calculating, and other aids to computation. Part of the Handbook for Automatic Computation book series (HDBKAUCO, volume 2) Abstract In an early paper in this series 4 Householder’s algorithm for the tridiagonalization of a real symmetric matrix was discussed.

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Chebyshev expansions for the error and related functions


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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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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[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]
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[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]
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[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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Pdf J.h.wilkinson C.reinsch Handbook For Automatic Computation Pdf Download

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