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Lecture23

# Lecture23 - IE 495 Lecture 23 Reading for This Lecture...

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IE 495 Lecture 23 November 21, 2000

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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

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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".

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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?

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Lecture23 - IE 495 Lecture 23 Reading for This Lecture...

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