Convergence Rates for Multivariate Smoothing Spline Functions.

Abstract

Smoothing splines are used to approximate smooth functions when there are only available noisy values of the function at discrete values of the independent variables. It is shown herein that as the grid of values of the independent variables becomes denser in the region of interest, the smoothing spline estimate approaches the true function. Results on the rate of this convergence are given. Convergence of derivatives is investigated, also, but under the assumption that the region is bounded. The theory of linear elliptic partial differential equations is used extensively, along with eigenvalue approximation methods. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1982
Accession Number
ADA124368

Entities

People

  • Dennis D. Cox

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Banach Space
  • Boundary Value Problems
  • Convergence
  • Differential Equations
  • Distribution Functions
  • Eigenvalues
  • Equations
  • Partial Differential Equations
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Random Variables
  • Statistics
  • Stochastic Processes
  • Three Dimensional
  • Two Dimensional
  • United States

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)