ON THE Relationship between Functions with the Same Optimal Knots in Spline with Piecewise Polynomial Approximation.

Abstract

The relationship between functions with the same optimal knows for L sub 2 (0,1) approximation by k-th order splines or piecewise polynomials is investigated. It is shown that, if two functions have positive continuous k-th derivatives, they will have the same optimal knots if and only if they differ by a polynomial of order k. An application to design selection for continuous time regression is considered and extensions to L sub p approximation are also provided. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1982
Accession Number
ADA125002

Entities

People

  • Randall L. Eubank

Organizations

  • Southern Methodist University

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Communities of Interest

  • Materials and Manufacturing Processes

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Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Regression Analysis.