Lecture 15 - 51 Least Squares Approximates k for creatures freakin f Approximation Discrete Least Sgooes norm using seel Gwen Cxc f CXnifn Example

Lecture 15 - 51 Least Squares Approximates k for...

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k 51 Least Squares Approximates using norm for creatures freakin f seel Discrete Least Sgooes Approximation Gwen Cxc f CXnifn want to ft data Example want 0 approximate by a line y Ao ta X Deane 2 G 33 Elana Fk Cao 19 XD Minimum 5134 2 2k Cao taxed C l D 5 35 Zao 2 Cao ca xD EX'd O Za then obtain Eg 5367 90 19 Fk f 37 a x taiNq E k 9 linear approximation
want best Prix got a X t an X kN l want nccN 5.38 Ela uan Fk Cao exe e Anfal get Normal Equations 5.39 jzoaj x It XE fo moi in matrix d coeltients for the linear system symmetry postine definite and highly sensitive In small perturbations in the data Increases degree of approximating polynomial cannot use earlier approximatii Solution use orthogonality
weighted discrete inner product E 90 Lf g7 µ fixe gCXe wk we O for K l N weights On polynomials fj is of degree exaetyj Then we Ran write

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