CSC_349_HANDOUT#6 - COMPUTER SCIENCE 349A Handout Number 6...

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1 COMPUTER SCIENCE 349A Handout Number 6 CONDITION OF A PROBLEM Definition A problem whose (exact) solution can change greatly with small changes in the data defining the problem is called ill-conditioned . data { d i } exact solution { r i } defining a problem exact arithmetic perturbed problem, data { ˆ d i } = { d i + ε i } exact solution { ˆ r i } with i d i small exact arithmetic If there exist small i such that { ˆ r i } are not close to { r i }, then the problem is ill-conditioned . If {} {} i i r r ˆ for all small i , then the problem is well-conditioned . Example Consider the 3 × 3 system of linear equations b Hx = : = 60 / 47 12 / 13 6 / 11 5 / 1 4 / 1 3 / 1 4 / 1 3 / 1 2 / 1 3 / 1 2 / 1 1 3 2 1 x x x . Using the exact {} i d given above in the matrix H and the vector b , the exact solution is = 1
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This note was uploaded on 12/10/2011 for the course CSC 349 taught by Professor Oadje during the Spring '11 term at University of Victoria.

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CSC_349_HANDOUT#6 - COMPUTER SCIENCE 349A Handout Number 6...

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