xn 1 3 1 7 27 7 5 2p y1 1 6 y2p1 6 y6 4 p yn 1

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Unformatted text preview: x, y be perturbations, i.e., ^ x=x+ x 7 ^ y=y+ y 3 1 7 27 7 (6b) 5 n Backward Error Analysis Observe that Thus, p 1+ k 2 = 1 + k =2 + O( k ) 2 3 2 x ( =2 + O( )) 6 x1( 1=2 + O( 12)) 7 6 7 2 x=6 2 2 . 7 . 4 5 2 xn( n=2 + O( n)) But j kj nu + O(u2), so j xj nu jxj + O(u2) (7a) j yj nu jyj + O(u2) (7b) and 2 2 These bounds are very conservative 8...
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This document was uploaded on 03/16/2014 for the course CSCI 6800 at Rensselaer Polytechnic Institute.

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