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Rate of convergence of discretization in Chebyshev approximation


Authors: C. B. Dunham and Jack Williams
Journal: Math. Comp. 37 (1981), 135-139
MSC: Primary 41A25; Secondary 30E10, 41A50, 65D15
DOI: https://doi.org/10.1090/S0025-5718-1981-0616366-X
MathSciNet review: 616366
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Abstract: The paper treats, in a particularly simple fashion, the practical problem of the rate of convergence of discretization in real and complex Chebyshev approximation. Both linear and nonlinear approximations are discussed and, subject to certain conditions, quadratic convergence of the discretizations is obtained along with an explicit rate constant which can be estimated numerically.


References [Enhancements On Off] (What's this?)

  • [1] B. A. Chalmers, "On the rate of convergence of discretization in Chebyshev approximation," SIAMJ. Numer. Anal., v. 15, 1978, pp. 612-617. MR 0494836 (58:13620)
  • [2] E. W. Cheney, Introduction to Approximation Theory, McGraw-Hill, New York, 1966. MR 0222517 (36:5568)
  • [3a] C. B. Dunham, "Rational approximation on subsets," J. Approx. Theory, v. 1, 1968, pp. 484-487. MR 0238002 (38:6279)
  • [3b] C. B. Dunham, "Approximation by alternating families on subsets," Computing, v. 9, 1972, pp. 261-265. MR 0312686 (47:1242)
  • [3c] C. B. Dunham, "Alternating Chebyshev approximation," Trans. Amer. Math. Soc., v. 178, 1973, pp. 95-109. MR 0318736 (47:7282)
  • [3d] C. B. Dunham, "Varisolvent Chebyshev approximation on subsets," in Approximation Theory (G. G. Lorentz, Ed.), Academic Press, New York, 1973, pp. 337-340. MR 0333534 (48:11859)
  • [3e] C. B. Dunham, "Efficiency of Chebyshev approximation on finite subsets," J. Assoc. Comput. Mach., v. 21, 1974, pp. 311-313. MR 0367527 (51:3769)
  • [3f] C. B. Dunham, "Dependence of best rational Chebyshev approximations on the domain," Canad. Math. Bull., v. 20, 1977, pp. 451-454. MR 0487190 (58:6850)
  • [4] S. Ellacott & Jack Williams, "Linear Chebyshev approximation in the complex plane using Lawson's algorithm," Math. Comp., v. 30, 1976, pp. 35-44. MR 0400652 (53:4483)
  • [5] G. G. Lorentz, Approximation of Functions, Holt, Rinehart and Winston, New York, 1966. MR 0213785 (35:4642)
  • [6] E. B. Saff & R. S. Varga, "Nonuniqueness of best approximating complex rational functions," Bull. Amer. Math. Soc., v. 83, 1977, pp. 375-377. MR 0433108 (55:6087)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1981-0616366-X
Article copyright: © Copyright 1981 American Mathematical Society

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