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Best $ L\sb{p}$ approximation

Author: S. W. Kahng
Journal: Math. Comp. 26 (1972), 505-508
MSC: Primary 65D15
MathSciNet review: 0309270
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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 [Enhancements On Off] (What's this?)

  • [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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Keywords: Polynomial approximation, Newton-Raphson method
Article copyright: © Copyright 1972 American Mathematical Society

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