Rate of convergence of Lawson's algorithm

Author:
A. K. Cline

Journal:
Math. Comp. **26** (1972), 167-176

MSC:
Primary 65D15

DOI:
https://doi.org/10.1090/S0025-5718-1972-0298872-8

MathSciNet review:
0298872

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Abstract: The algorithm of Charles L. Lawson determines uniform approximations of functions as limits of weighted approximations. Lawson noticed from experimental evidence that the algorithm seemed to converge linearly and convergence was related to a factor which was the ratio of the largest nonmaximum error of the best uniform approximation to the maximum error. This paper proves the linear convergence and explores the relation of the rate of convergence to this ratio.

**[1]**A. K. Cline,*Uniform Approximation as a Limit of Approximations*, Ph.D. Thesis, University of Michigan, Ann Arbor, Mich., 1970.**[2]**C. L. Lawson,*Contributions to the Theory of Linear Least Maximum Approximation*, Ph.D. Thesis, University of California, Los Angeles, Calif., 1961.**[3]**J. R. Rice,*The Approximation of Functions*. Vol. II:*Nonlinear and Multivariate Theory*, Addison-Wesley, Reading, Mass., 1969, pp. 298-304. MR**39**#5989. MR**0244675 (39:5989)****[4]**J. R. Rice & K. H. Usow, ``The Lawson algorithm and extensions,''*Math. Comp.*, v. 22, 1968, pp. 118-127. MR**38**#463. MR**0232137 (38:463)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1972-0298872-8

Keywords:
Uniform approximation,
least squares approximation

Article copyright:
© Copyright 1972
American Mathematical Society