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class_11 - CS205 Class 11 Covered in class: Everything...

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CS205 – Class 11 Covered in class : Everything Readings : Shewchuk Paper on course web page and Heath 473-478 1. Conjugate Directions a. The goal is to choose a sequence of search directions 0 s , 1 s , … that are all orthogonal. Then only one step is needed in each search direction b. We update 1 k k k k x x s where each k is chosen so that all the remaining error is orthogonal to the search direction k s . That is, 1 0 k k e s and we never need to step in the k s direction again. i. Note that 1 k k k k x x s leads to 1 k exact k exact k k x x x x s or 1 k k k k e e s (we’ll use this later too!) ii. 1 0 k k e s leads to   0 k k k k e s s or k k k k k e s s s   1. however we don’t know k e c. Just as before, instead of using e, we can use r=-Ae to obtain 1 0 k k r s or 1 0 k k Ae s i. This leads to   0 k k k k A e s s or
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class_11 - CS205 Class 11 Covered in class: Everything...

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