Lecture 13.pdf - Approximation Chapters Least Squares of degree In suchthat polynomial a pn Find fab 5D for a least continuous function f p Ao Cx to

# Lecture 13.pdf - Approximation Chapters Least Squares of...

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Chapters Least Squares Approximation SlcortinuousleastsquaresApproximat Find a polynomial pn of degree In suchthat 5 D fab pnex 2dx min for a continuous function f on Carb least squares Approximation to f let a I i p Cx Ao e ai X y x c Calls want minimize f Cao can fbaffexs p.cn Jdk fab fkxldx 2fabfcxicaoeaixldxtfabeaota.DK Note E Cao ai is quadratic this the minima must be a critical point derivatre will be zero 2El9oc9 b Tao Z fafcxidx 2faaotaixsdx OZEG.ca Tq 2 abxfexjdx 2fkaota.HR dx o 2 2 Gives linear system for ao ca B 3 Sablon a c abXdx a Sabfcxidx 15.4 sabxdxjaotfsabxdxgg fabxfcxi.dk Normal Equation for a I
9 Exaw cetfcx.ee forxECoiD then 5.5 Solaxidx So exdx e I 5 6 Sol fc id f xe dx I then the normal equations G 7 got a a e I G 8 got 139,21 solve to get 90 4 e lo 9 Cee 118 Pix ge lo e 18 6 e X is the least squares approximek to feed _e by a linear polynomial in cost Figure 5 I
least squares approximation thehoest approximetm in the U2 norm Pn is the least squares qpproximrtho to a function