chapter3.page18

# chapter3.page18 - 1 1 1 . 1 we get diﬀerent solu-tion,...

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18 1. BRIEF INTRODUCTION TO VECTORS AND MATRICES (2) Condition Number In solving Ax = b , one number is very important, it is called the condition number, which can be de- ﬁned as C ( A ) = | s l , where λ s is the eigenvalue with smallest absolute value and lambda l is the eigenvalue with largest ab- solute value, if C ( A ) is too large or too small, a little change in b will result in a large in the solution x. We say the system Ax = b is not stable. Now if A = 1 1 2 1 3 1 2 1 3 1 4 1 3 1 4 1 5 Find all eigenvalues, all eigenvectors, and C ( A ) . Find solution of Ax = b if b = 1 1 1 Change b a little to b =
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Unformatted text preview: 1 1 1 . 1 we get diﬀerent solu-tion, which component of the new solution change most? The change of the third component if 10% what is the percentage change of the most changed component? Note: • Our deﬁnition of condition number is not accurate, the true deﬁnition is C ( A ) = 1 k A kk A-1 k where k · k is a given norm (metric). • Mathcad provides three functions cond 1( A ) , cond 2( A ) and condi ( A ) in compute condition number for A in diﬀerent metric....
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## This note was uploaded on 10/04/2011 for the course MAP 4231 taught by Professor Dr.han during the Spring '11 term at UNF.

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