chapter3.page18

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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 =
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

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.

Ask a homework question - tutors are online