Rate of convergence of Lawson’s algorithm
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- by A. K. Cline PDF
- Math. Comp. 26 (1972), 167-176 Request permission
Abstract:
The algorithm of Charles L. Lawson determines uniform approximations of functions as limits of weighted ${L_2}$ 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.References
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A. K. Cline, Uniform Approximation as a Limit of ${L_2}$ Approximations, Ph.D. Thesis, University of Michigan, Ann Arbor, Mich., 1970.
C. L. Lawson, Contributions to the Theory of Linear Least Maximum Approximation, Ph.D. Thesis, University of California, Los Angeles, Calif., 1961.
- 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
- John R. Rice and Karl H. Usow, The Lawson algorithm and extensions, Math. Comp. 22 (1968), 118–127. MR 232137, DOI 10.1090/S0025-5718-1968-0232137-4
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Math. Comp. 26 (1972), 167-176
- MSC: Primary 65D15
- DOI: https://doi.org/10.1090/S0025-5718-1972-0298872-8
- MathSciNet review: 0298872