Global Approximation Results

  • Claudio Canuto
  • M. Yousuff Hussaini
  • Alfio Quarteroni
  • Thomas A. ZangJr.
Part of the Springer Series in Computational Physics book series (SCIENTCOMP)

Abstract

In this chapter we present error estimates for the approximation of functions by orthogonal polynomials. The results will cover the following topics:
  1. (i)

    inverse inequalities for polynomials concerning summability and differentiability;

     
  2. (ii)

    error estimates for the truncation error uP N u,where P N u denotes the truncated “Fourier” series of u;

     
  3. (iii)

    existence, uniqueness and error estimates for the polynomials of best approximation in L P or Sobolev norms;

     
  4. (iv)

    error estimates for the interpolation error uI N u,where I N u denotes the polynomial interpolating u at a selected set of points in the domain.

     

Keywords

Assure Peri INuliN Aliasing NUllo 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Claudio Canuto
    • 1
  • M. Yousuff Hussaini
    • 2
  • Alfio Quarteroni
    • 3
  • Thomas A. ZangJr.
    • 4
  1. 1.Dipartimento di MatematicaPolitecnico di TorinoTorinoItaly
  2. 2.ICASE. Mail Stop 132CNASA Langley Research CenterHamptonUSA
  3. 3.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  4. 4.Mail Stop 159 Computational Sciences BranchNASA Langley Research CenterHamptonUSA

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