Lecture23 - IE 495 Lecture 23 November 21, 2000 Reading for...

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Unformatted text preview: IE 495 Lecture 23 November 21, 2000 Reading for This Lecture Primary Miller and Boxer, Pages 128-134 Forsythe and Mohler, Sections 9-13 Parallel Gaussian Elimination PRAM with n 2 processors Mesh with n 2 processors Scaling In the "bad" example from the last lecture, what caused the trouble? Essentially, coefficients were too far apart in "scale". Ex: 10 5 + 10-5 = 10 5 if d = 5 . What can we do about this? Diagonal Equivalence Two matrices A and A are diagonally equivalent if A = D 1-1 AD 2 D 1 and D 2 are non-singular diagonal matrices A is just A with the columns and rows "scaled". For our purposes, the elements of D 1 and D 2 will be powers of 10 (we assume this base). Hence, this operation merely changes the exponent. This operation does not change the "significands". Computing with Scaled Matrices Notice that "diagonal equivalence" is an equivalence relation. Suppose we set b = D 1 b (similarly scaled) If the same sequence of pivots is used, The solutions to the these systems will have the same significands: A x = b Ax = b They will differ only in their exponents. What is the point?What is the point?...
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This note was uploaded on 08/06/2008 for the course IE 495 taught by Professor Linderoth during the Fall '08 term at Lehigh University .

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Lecture23 - IE 495 Lecture 23 November 21, 2000 Reading for...

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