Polynomial Interpolation of Real Functions 1: Interpolation in an Interval

Abstract

This paper is the first in a series to analyses the accuracy of polynomial interpolation of functions and its dependence on the locations of the interpolation nodes. It surveys known results for polynomial interpolation in an interval. It also introduces the concept of the Minimal Interpolation Sets which are the 'optimal' interpolation sets. New results concerning the properties of the minimal sets as well as procedures for locating the minimal sets are presented. The table for the minimal sets in the L- norm is given. An adaptive scheme for determining the interpolation order is also presented. Examples show the efficacy of this approach.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1993
Accession Number
ADA272330

Entities

People

  • Ivo Babuška
  • Qi Chen

Organizations

  • University of Maryland

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Chebyshev Polynomials
  • Computations
  • Continuity
  • Errors
  • Estimators
  • Finite Element Analysis
  • Government (Foreign)
  • Inequalities
  • Interpolation
  • Intervals
  • Maryland
  • Mathematics
  • Polynomials
  • Standards
  • Triangles
  • Universities

Fields of Study

  • Mathematics

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)