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9 - Polynomial Interpolation

from Part II - Constructive Approximation Theory

Published online by Cambridge University Press:  29 September 2022

Abner J. Salgado  and
Steven M. Wise
Abner J. Salgado
Affiliation:
University of Tennessee, Knoxville
Steven M. Wise
Affiliation:
University of Tennessee, Knoxville
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Summary

We study the problem of polynomial interpolation. Its solution with the Vandermonde matrix, and with a Lagrange nodal basis are then presented, and error estimates are provided. The Runge phenomenon is then illustrated. Hermite interpolation then is studied, its solution is given, and error estimates are provided. The problem of Lagrange interpolation is then generalized to the case of holomorphic functions on the complex plane, and error estimates are provided. A more efficient construction, via divided differences, is then given for the interpolating polynomial. We extend the notion of divided differences, in order to use them to provide error estimates for polynomial interpolation.

Keywords

Vandermonde matrixLagrange interpolationLagrange nodal basisRunge phenomenonHermite interpolationdivided differences
Type
Chapter
Information
Classical Numerical Analysis
A Comprehensive Course
 , pp. 231 - 265
Publisher: Cambridge University Press
Print publication year: 2022

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