Lecture Notes 14

Lecture Notes 14 - Lecture14 Lecture 14 Gram-Schmidt...

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Lecture14 1 Outline: 1) Review GS for taking A to Q Examples galore 2) Gram-Schmidt orthogonalization leads to a new factorization A=QR 3) Using the QR to solve Linear Least-squares problems 4) Matlab 5) Computational issues, algorithms (modified Gram-Schmidt), computational costs. .. 6) Quick review of course so far (end of the middle) Lecture 14: Gram-Schmidt Orthogonalization and the QR factorization Gram-Schmidt Orthogonalization: Example Illustration in R 2 1 2 3 1 2 Gram-Schmidt Orthogonalization: Example in R 3 : find an orthonormal basis for the C(A) where A = [ 1 1 1 ; 1 1 0; 1 0 0]; 1) Extension of general algorithm to n vectors Gram-Schmidt Orthogonalization: Example in R 3 : find an orthonormal basis for the C(A) where A = [ 1 1 1 ; 1 1 0; 1 0 0]; 2) Specific example
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Lecture14 2 Gram-Schmidt Orthogonalization: Example in R 3 : find an orthonormal basis for the C(A) where A = [ 1 1 1 ; 1 1 0; 1 0 0]; 3) Comment Q not unique: suppose A=[ 1 1 1; 0 1 1 ; 0 0 1] Gram-Schmidt Orthogonalization:
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This note was uploaded on 06/02/2010 for the course APMA APMA E3101 taught by Professor Spiegelman during the Fall '07 term at Columbia.

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Lecture Notes 14 - Lecture14 Lecture 14 Gram-Schmidt...

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