The Lp minimality and near-minimality of orthogonal polynomial approximation and integration methods

  • J. C. Mason
Part of the Lecture Notes in Mathematics book series (LNM, volume 1329)


It is known that the Chebyshev polynomials of the first and second kinds are minimal in Lp on [−1,1] with respect to appropriate weight functions, namely certain powers of 1−x2, for 1≤p≤∞. These properties are here exploited in two applications. First, convergence and optimality properties are established for a "complete" Chebyshev polynomial expansion method for the determination of indefinite integrals. Second, conjectures are derived concerning the near-minimality of the Laguerre polynomials L n ±1/2 (2β ×) for β≃1 with respect to appropriate exponentially weighted Lp norms on [0,∞).


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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • J. C. Mason
    • 1
  1. 1.Computational Mathematics GroupRoyal Military College of ScienceShrivenham, SwindonEngland

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