Best approximation

Author:
S. W. Kahng

Journal:
Math. Comp. **26** (1972), 505-508

MSC:
Primary 65D15

DOI:
https://doi.org/10.1090/S0025-5718-1972-0309270-2

MathSciNet review:
0309270

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Abstract | References | Similar Articles | Additional Information

Abstract: A new algorithm is presented for the best approximation of a continuous function over a discrete set or a finite interval with . Methods to accelerate the convergence of the Rice-Usow extension of Lawson's algorithm as well as the new algorithm are presented, and the result of a numerical example is given.

**[1]**C. L. Lawson,*Contribution to the Theory of Linear Least Maximum Approximations*, Ph.D. Thesis, University of California, Los Angeles, Calif., 1961, pp. 55-61.**[2]**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)****[3]**G. H. Hardy, J. E. Littlewood & G. Pólya,*Inequalities*, Cambridge Univ. Press, New York, 1934, p. 146.**[4]**J. M. Ortega & W. C. Rheinboldt,*Iterative Solution of Nonlinear Equations in Several Variables*, Academic Press, New York, 1970, pp. 501-506. MR**0273810 (42:8686)****[5]**J. R. Rice,*The Approximation of Functions*. Vol. I:*Linear Theory*, Addison-Wesley, Reading, Mass., 1964, p. 32. MR**29**#3795. MR**0166520 (29:3795)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1972-0309270-2

Keywords:
Polynomial approximation,
Newton-Raphson method

Article copyright:
© Copyright 1972
American Mathematical Society