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Unformatted text preview: Q T Q = I is an orthogonal matrix and is a diagonal matrix whose diagonal elements are positive and also are the eigenvalues of A . Dene x = Q T x and b = Q T b Ax = b and x = b Given x and x , dene the sequence x k as the sequence of vectors produced by steepest descent applied to Ax = b and the sequence x k as the sequence of vectors produced by steepest descent applied to x = b . Let e k = x k-x and e k = x k- x . Show that if x = Q T x then k e k k 2 = k e k k 2 , k > 1...
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This note was uploaded on 07/25/2011 for the course MAD 5403 taught by Professor Gallivan during the Spring '11 term at University of Florida.
- Spring '11