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# Annihilation Technique Suppose the n n matrix A has eigenvalues 1,... ,n ordered by |1| ISBN: 9780534392000 331

## Solution for problem 9.2.18 Chapter 9-2

Numerical Analysis (Available Titles CengageNOW) | 8th Edition

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Problem 9.2.18

Annihilation Technique Suppose the n n matrix A has eigenvalues 1,... ,n ordered by |1| > |2| > |3||n |, with linearly independent eigenvectors v(1) , v(2) ,... , v(n) . a. Show that if the Power method is applied with an initial vector x(0) given by x(0) = 2v(2) + 3v(3) ++ n v(n) , then the sequence {(m) } described in Algorithm 9.1 will converge to 2. b. Show that for any vector x = n i=1 iv(i) , the vector x(0) = (A 1 I)x satisfies the property given in part (a). c. Obtain an approximation to 2 for the matrices in Exercise 1. d. Show that this method can be continued to find 3 using x(0) = (A 2 I)(A 1 I)x

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1. How is total magnification of an image determined ­Objective magnificationx10 2. Determine population size using mark­recapture method ­N=(M1)(T2)/(M2) ­M1=# marked and released (given) ­M2=# marked counted ­T2= total number counted 3. Determine population size using removal sampling method ­Plot # removed each period on Y axis ­Plot # previously removed on...

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##### ISBN: 9780534392000

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