Linear Chebyshev approximation in the complex plane using Lawson's algorithm

Authors:
S. Ellacott and Jack Williams

Journal:
Math. Comp. **30** (1976), 35-44

MSC:
Primary 65D15

MathSciNet review:
0400652

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Abstract: In this paper we discuss the application of Lawson's algorithm for computing best linear Chebyshev approximations to complex-valued functions. Some numerical examples are also presented.

**[1]**E. W. Cheney,*Introduction to approximation theory*, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR**0222517****[2]**A. K. Cline,*Rate of convergence of Lawson’s algorithm*, Math. Comp.**26**(1972), 167–176. MR**0298872**, 10.1090/S0025-5718-1972-0298872-8**[3]**G. Golub,*Numerical methods for solving linear least squares problems*, Numer. Math.**7**(1965), 206–216. MR**0181094****[4]**C. L. LAWSON,*Contributions to the Theory of Linear Least Maximum Approximations*, Thesis, UCLA, 1961.**[5]**G. G. Lorentz,*Approximation of functions*, Holt, Rinehart and Winston, New York-Chicago, Ill.-Toronto, Ont., 1966. MR**0213785****[6]**John R. Rice,*The approximation of functions. Vol. 2: Nonlinear and multivariate theory*, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR**0244675****[7]**John R. Rice and Karl H. Usow,*The Lawson algorithm and extensions*, Math. Comp.**22**(1968), 118–127. MR**0232137**, 10.1090/S0025-5718-1968-0232137-4**[8]**T. J. Rivlin and H. S. Shapiro,*A unified approach to certain problems of approximation and minimization*, J. Soc. Indust. Appl. Math.**9**(1961), 670–699. MR**0133636****[9]**Jack Williams,*Numerical Chebyshev approximation in the complex plane*, SIAM J. Numer. Anal.**9**(1972), 638–649. MR**0314232**

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DOI:
https://doi.org/10.1090/S0025-5718-1976-0400652-0

Article copyright:
© Copyright 1976
American Mathematical Society