Linear Chebyshev approximation of complex-valued functions
I. Barrodale, L. M. Delves and J. C. Mason
Math. Comp. 32 (1978), 853-863
Primary 65D15; Secondary 41A50
Full-text PDF Free Access
Similar Articles |
Abstract: This paper is concerned with Chebyshev approximation by linear functions to complex-valued data. The problem is nonlinear, and we present a convergent algorithm for its solution. We also pose a related linear problem which is simple to solve, and which produces approximations which are near-best in the Chebyshev sense within a factor of . Some numerical examples are provided.
Barrodale and C.
Phillips, An improved algorithm for discrete Chebyshev linear
approximation, Proceedings of the Fourth Manitoba Conference on
Numerical Mathematics (Winnipeg, Man., 1974) Utilitas Math., Winnipeg,
Man., 1975, pp. 177–190. Congr. Numer., No. XII. MR 0373585
Collatz and W.
Wetterling, Optimization problems, Springer-Verlag, New
York-Heidelberg, 1975. Translated from the German by P. Wadsack; Applied
Mathematical Sciences, Vol. 17. MR 0377635
Ellacott and Jack
Williams, Linear Chebyshev approximation in the
complex plane using Lawson’s algorithm, Math. Comput. 30 (1976), no. 133, 35–44. MR 0400652
(53 #4483), http://dx.doi.org/10.1090/S0025-5718-1976-0400652-0
O. Geddes and J.
C. Mason, Polynomial approximation by projections on the unit
circle, SIAM J. Numer. Anal. 12 (1975),
111–120. MR 0364977
Numerical methods for constrained optimization, Academic Press,
London-New York, 1974. Edited by P. E. Gill and W. Murray. MR 0395227
C. L. LAWSON, Contributions to the Theory of Linear Least Maximum Approximations, Thesis, Univ. of California, Los Angeles, 1961.
G. Lorentz, Approximation of functions, Holt, Rinehart and
Winston, New York-Chicago, Ill.-Toronto, Ont., 1966. MR 0213785
Rabinowitz, Mathematical programming and approximation,
Approximation Theory (Proc. Sympos., Lancaster, 1969) Academic Press,
London, 1970, pp. 217–231. MR 0267896
D. M. SIMMONS, Nonlinear Programming for Operations Research, Prentice-Hall, Englewood Cliffs, N. J., 1975, (Chapter 9).
W. I. ZANGWILL, Nonlinear Programming, Prentice-Hall, Englewood Cliffs, N. J., 1969, (Chapter 14).
I. Zukhovitskiy and L.
I. Avdeyeva, Linear and convex programming, Translated from
the Russian by Scripta Technica, Inc. Edited by Bernard R. Gelbaum, W. B.
Saunders Co., Philadelphia, Pa.-London, 1966. MR 0226936
- I. BARRODALE & C. PHILLIPS, Algorithm 495--Solution of an Overdetermined System of Linear Equations in the Chebyshev Norm, ACM Trans. Math. Software, v. 1, 1975, pp. 264-270. MR 0373585 (51:9785)
- L. COLLATZ & W. WETTERLING, Optimization Problems, Springer-Verlag, Berlin and New York, 1975, pp. 278-280. MR 0377635 (51:13806)
- S. ELLACOTT & JACK WILLIAMS, "Linear Chebyshev approximation in the complex plane using Lawson's algorithm," Math. Comp., v. 30, 1976, pp. 35-44. MR 0400652 (53:4483)
- K. O. GEDDES & J. C. MASON, "Polynomial approximation by projections on the unit circle," SIAM J. Numer. Anal., v. 12, 1975, pp. 111-120. MR 0364977 (51:1230)
- P. E. GILL & W. MURRAY, Numerical Methods for Constrained Optimization, Academic Press, New York, 1974. MR 0395227 (52:16025)
- C. L. LAWSON, Contributions to the Theory of Linear Least Maximum Approximations, Thesis, Univ. of California, Los Angeles, 1961.
- G. G. LORENTZ, Approximation of Functions, Holt, Rinehart and Winston, New York,1966. MR 0213785 (35:4642)
- P. RABINOWITZ, "Mathematical programming and approximation," in Approximation Theory, A. Talbot (Editor), Academic Press, New York, 1970, pp. 217-231. MR 0267896 (42:2797)
- D. M. SIMMONS, Nonlinear Programming for Operations Research, Prentice-Hall, Englewood Cliffs, N. J., 1975, (Chapter 9).
- W. I. ZANGWILL, Nonlinear Programming, Prentice-Hall, Englewood Cliffs, N. J., 1969, (Chapter 14).
- S. I. ZUKHOVITSKIY & L. I. AVDEYEVA, Linear and Convex Programming, Saunders, Philadelphia, 1966, (Chapter 6). MR 0226936 (37:2522)
Retrieve articles in Mathematics of Computation
Retrieve articles in all journals
© Copyright 1978
American Mathematical Society