Linear Chebyshev approximation of complex-valued functions

Authors:
I. Barrodale, L. M. Delves and J. C. Mason

Journal:
Math. Comp. **32** (1978), 853-863

MSC:
Primary 65D15; Secondary 41A50

DOI:
https://doi.org/10.1090/S0025-5718-1978-0483298-X

MathSciNet review:
0483298

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

**[1]**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)****[2]**L. COLLATZ & W. WETTERLING,*Optimization Problems*, Springer-Verlag, Berlin and New York, 1975, pp. 278-280. MR**0377635 (51:13806)****[3]**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)****[4]**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)****[5]**P. E. GILL & W. MURRAY,*Numerical Methods for Constrained Optimization*, Academic Press, New York, 1974. MR**0395227 (52:16025)****[6]**C. L. LAWSON,*Contributions to the Theory of Linear Least Maximum Approximations*, Thesis, Univ. of California, Los Angeles, 1961.**[7]**G. G. LORENTZ,*Approximation of Functions*, Holt, Rinehart and Winston, New York,1966. MR**0213785 (35:4642)****[8]**P. RABINOWITZ, "Mathematical programming and approximation," in*Approximation Theory*, A. Talbot (Editor), Academic Press, New York, 1970, pp. 217-231. MR**0267896 (42:2797)****[9]**D. M. SIMMONS,*Nonlinear Programming for Operations Research*, Prentice-Hall, Englewood Cliffs, N. J., 1975, (Chapter 9).**[10]**W. I. ZANGWILL,*Nonlinear Programming*, Prentice-Hall, Englewood Cliffs, N. J., 1969, (Chapter 14).**[11]**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*
with MSC:
65D15,
41A50

Retrieve articles in all journals with MSC: 65D15, 41A50

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1978-0483298-X

Article copyright:
© Copyright 1978
American Mathematical Society