Optimal Approximation of Linear Operators

  • Anatoly Yu. Bezhaev
  • Vladimir A. Vasilenko
Chapter

Abstract

In this chapter, we introduce the general problem of optimal approximation of a linear operator by the value of another operator. The spline interpolating method helps us to solve this problem and to obtain numerical formulas of optimal approximation for a wide variety of functional spaces and linear operators. More exactly, it is possible when the reproducing kernels or mappings are known and effectively calculated. Besides, in these cases the exact estimates of errors on classes and extremal elements can be obtained, too.

Keywords

Linear Operator Optimal Approximation Variational Theory Prolongation Method Approximation Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Anatoly Yu. Bezhaev
  • Vladimir A. Vasilenko
    • 1
  1. 1.Institute of Computational Mathematics and Mathematical GeophysicsNovosibirskRussia

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