Unformatted text preview: A . (If this is too analytic for your taste, then change to the basis { v 1 , v 2 , . . . , v n } . Under this basis A has coordinates Λ = diag( λ 1 , λ 2 , . . . , λ n ), and Λ k y → e 1 as long as y (1) 6 = 0.) The power method consists of scaling iteration (2) to avoid underﬂow or overﬂow, and ﬁguring out when to stop. We solve both problems by approximating λ 1 at each step. The code below (if it terminates) gives a small backward error (i.e. gives an eigenpair for a matrix “close” to A ). i = argmax(  x  ) x = x/x ( i ) For k = 1 , 2 , . . . until done y = Ax i = argmax(  y  ) λ = y ( i ) r = yλx , if k r k is small enough, then stop x = y/λ...
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 Fall '10
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 Linear Algebra, Power, Eigenvalue, eigenvector and eigenspace, Generalized eigenvector, linearly independent eigenvectors, dominant eigenvector

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