Efficiency of a Procedure for Near-Minimax Approximation

ABSTRACT

A procedure using the minimax polynomial fit of degree n on the set of extrema of the Chebyshev polynomial Tn+1 is examined for its effectiveness in generating near-minimax fits on [-1, 1]. It is compared to Powell's results for interpolation at the zeros of Tn.

REFERENCES

• 1: POWELL, M. J. D. On the maximum errors of polynomial approximations defined by interpolation and by least squares criteria: Comput. J. 9 (1967), 404--407.
• 2: ZURMUHL, R. Zur angenherten ganzrationalen Tschebysheff--Approximation mit I-Iflfe trigonometrischer Interpolation. Numer. Math. 6 (1964), 1-5.
• 3: W. Fraser, A Survey of Methods of Computing Minimax and Near-Minimax Polynomial Approximations for Functions of a Single Independent Variable, Journal of the ACM (JACM), v.12 n.3, p.295-314, July 1965 [doi>10.1145/321281.321282]
• 4: W. Fraser , J. F. Hart, Remark on algorithm 162: Near-minimax polynomial approximations and partitioning of intervals, Communications of the ACM, v.7 n.8, p.486-489, Aug. 1964 [doi>10.1145/355586.364820]
• 5: MEINARDUS, G. Approximation of Functions: Theory and Numerical Methods. Springer, New York, 1967.
• 6: HORNFVrER, G. Mthodes pratiques pour la dtermination approche de la meilleure approximation polynSmiale ou rationnelle. Chiffres $ (1960), 193-228.
• 7: FOX, L., AND PARKER, I .B . Chebyshev Polynomials in Numerical Analysis. Oxford U. Press, London, 1968.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.2 Approximation
          Subjects: Minimax approximation and algorithms

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.1 Interpolation
          Subjects: Interpolation formulas

General Terms:
Measurement, Performance, Theory