|
Numerical Chebyshev approximation by interpolating rationals
Author:
Jack Williams
Journal:
Math. Comp. 26 (1972), 199-206
MSC:
Primary 65D15
MathSciNet review:
0373230
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: The paper is concerned with the Chebyshev approximation of decay-type functions  by interpolating rationals. The interpolating points are chosen to be the zeros of  . Existence, uniqueness and characterization of best approximations are first shown. An exchange algorithm is then described for computing the best approximation.
- [1]
K. Appel, ``Rational approximation of decay-type functions,'' Nordisk Tidskr. Informationsbehandling, v. 2, 1962, pp. 69-75.
- [2]
D.
C. Handscomb (ed.), Methods of numerical approximation,
Pergamon Press, Oxford, 1966. Lectures delivered at a Summer School held at
Oxford University, Oxford, September, 1965. MR 0455292
(56 #13531)
- [3]
Cecil
Hastings Jr., Approximations for digital computers, Princeton
University Press, Princeton, N. J., 1955. Assisted by Jeanne T. Hayward and
James P. Wong, Jr. MR 0068915
(16,963e)
- [4]
Günter
Meinardus, Approximation of functions: Theory and numerical
methods, Expanded translation of the German edition. Translated by
Larry L. Schumaker. Springer Tracts in Natural Philosophy, Vol. 13,
Springer-Verlag New York, Inc., New York, 1967. MR 0217482
(36 #571)
- [5]
John
R. Rice, The approximation of functions. Vol. I: Linear
theory, Addison-Wesley Publishing Co., Reading, Mass.-London, 1964. MR 0166520
(29 #3795)
- [6]
J. Williams, Some Numerical Problems in Theoretical Physics, Doctoral Thesis, University of Oxford, Oxford, 1968.
- [1]
- K. Appel, ``Rational approximation of decay-type functions,'' Nordisk Tidskr. Informationsbehandling, v. 2, 1962, pp. 69-75.
- [2]
- D. C. Handscomb, Methods of Numerical Approximation, Pergamon Press, London, 1966. MR 0455292 (56:13531)
- [3]
- C. Hastings, Approximations for Digital Computers, Princeton Univ. Press, Princeton, N. J., 1955. MR 16, 963. MR 0068915 (16:963e)
- [4]
- G. Meinardus, Approximation of Functions: Theory and Numerical Methods, Springer, Berlin, 1964; English transl., Springer Tracts in Natural Philosophy, vol. 13, Springer-Verlag, New York, 1967. MR 31 #547; MR 36 #571. MR 0217482 (36:571)
- [5]
- John R. Rice, The Approximation of Functions. Vol. I: Linear Theory, AddisonWesley, Reading, Mass., 1964. MR 29 #3795. MR 0166520 (29:3795)
- [6]
- J. Williams, Some Numerical Problems in Theoretical Physics, Doctoral Thesis, University of Oxford, Oxford, 1968.
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
65D15
Retrieve articles in all journals
with MSC:
65D15
Additional Information
DOI:
http://dx.doi.org/10.1090/S0025-5718-1972-0373230-6
PII:
S 0025-5718(1972)0373230-6
Keywords:
Chebyshev approximation,
exchange algorithm
Article copyright:
© Copyright 1972 American Mathematical Society
|
