2-04-08 - Interpolation Discreteanalysis o

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Unformatted text preview: Interpolation Discreteanalysis o Goal:Findcontinuousfunctionsfromdiscretedata o Linearinterpolation Letxi<x<xi+1 3.5 Knowyi=f(xi) 3 yi+1=f(xi+1) 2.5 Question:y=f(x)? 2 1.5 1 0.5 0 x x+1 x+2 x+3 2/4/08 y=yi+(yi+1yi)((xxi)/(xi+1xi)) =f(x) Nonlinearinterpolation Series1 x+4 Polynomialinterpolation Generalnthorderpolynomial Pn(x)=a0+a1x+a2x2 ++anxn allai(n+1ofthem)areunknownconstants canNitannthorderpolynomialton+1points (inthiscase,Nitmeans`goesthrough') Procedure WritePn(x)=a0+a1x+a2x2 ++anxn Foreach(xi,yi) Getn+1(linear)eqninn+1unknowns Solveforai's Linearalgebraproblem Example ...
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This note was uploaded on 04/07/2008 for the course EN 530.101.02 taught by Professor Okamura during the Spring '08 term at Johns Hopkins.

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