# Lecture28 - CMPSC/MATH 451 Numerical Computations Lecture 28 Prof Kamesh Madduri Class Overview Interpolation • Piecewise polynomial

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Unformatted text preview: CMPSC/MATH 451 Numerical Computations Lecture 28 October 24, 2011 Prof. Kamesh Madduri Class Overview: Interpolation • Piecewise polynomial interpolation • Cubic Hermite interpolation • Cubic spline interpolation • Octave tutorial 2 Interpolation Polynomial Interpolation Piecewise Polynomial Interpolation Piecewise Polynomial Interpolation Hermite Cubic Interpolation Cubic Spline Interpolation Piecewise Interpolation, continued Simplest example is piecewise linear interpolation, in which successive pairs of data points are connected by straight lines Although piecewise interpolation eliminates excessive oscillation and nonconvergence, it appears to sacrifice smoothness of interpolating function We have many degrees of freedom in choosing piecewise polynomial interpolant, however, which can be exploited to obtain smooth interpolating function despite its piecewise nature < interactive example > Michael T. Heath Scientific Computing 41 / 56 Interpolation Polynomial Interpolation Piecewise Polynomial Interpolation Piecewise Polynomial Interpolation Hermite Cubic Interpolation Cubic Spline Interpolation Hermite Interpolation In Hermite interpolation , derivatives as well as values of interpolating function are taken into account Including derivative values adds more equations to linear system that determines parameters of interpolating function To have unique solution, number of equations must equal number of parameters to be determined Piecewise cubic polynomials are typical choice for Hermite interpolation, providing flexibility, simplicity, and efficiency Michael T. Heath Scientific Computing 42 / 56 Interpolation Polynomial Interpolation Piecewise Polynomial Interpolation...
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## This note was uploaded on 01/19/2012 for the course CMPSC 451 taught by Professor Staff during the Spring '08 term at Pennsylvania State University, University Park.

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Lecture28 - CMPSC/MATH 451 Numerical Computations Lecture 28 Prof Kamesh Madduri Class Overview Interpolation • Piecewise polynomial

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