Best $L_{p}$ approximation
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- by S. W. Kahng PDF
- Math. Comp. 26 (1972), 505-508 Request permission
Abstract:
A new algorithm is presented for the best ${L_p}$ approximation of a continuous function over a discrete set or a finite interval with $2 < p < \infty$. 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.References
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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.
- 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 G. H. Hardy, J. E. Littlewood & G. Pólya, Inequalities, Cambridge Univ. Press, New York, 1934, p. 146.
- J. M. Ortega and W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Academic Press, New York-London, 1970. MR 0273810
- John R. Rice, The approximation of functions. Vol. I: Linear theory, Addison-Wesley Publishing Co., Reading, Mass.-London, 1964. MR 0166520
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Math. Comp. 26 (1972), 505-508
- MSC: Primary 65D15
- DOI: https://doi.org/10.1090/S0025-5718-1972-0309270-2
- MathSciNet review: 0309270