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Integration and approximation of multivariate functions: average case complexity with isotropic Wiener measure

Grzegorz W. Wasilkowski

Abstract

We study the average case complexity of multivariate integration and $L_2$ function approximation for the class $F=C([0,1]^d)$ of continuous functions of $d$ variables. The class $F$ is endowed with the isotropic Wiener measure (Brownian motion in Levy's sense). Furthermore, for both problems, only function values are used as data.

Integration and approximation of multivariate functions: average case complexity with isotropic Wiener measure

Abstract

We study the average case complexity of multivariate integration and function approximation for the class of continuous functions of variables. The class is endowed with the isotropic Wiener measure (Brownian motion in Levy's sense). Furthermore, for both problems, only function values are used as data.

Paper Structure

This paper contains 3 theorems, 15 equations.

Key Result

Theorem 1

For the integration and function approximation problems,

Theorems & Definitions (6)

  • Theorem 1
  • Theorem 2
  • Remark 1
  • Remark 2
  • Theorem 3
  • Remark 3