Write an algorithm that estimates the desired eigenvalues of an input matrix by

Question

Write an algorithm that estimates the desired eigenvalues of an input matrix by using the power method. Your algorithm must find the i^th largest eigenvalues by using the power method and deflation to remove an already determined dominant eigenvalues. Save your algorithm as "LastnamePM.m." Your algorithm must be a function of A (input matrix), n (the number of iterations), and i (the i^th largest eigenvalues). For example, if you call "LastnamePM(A, 10,3)", the outcome will be the estimated 3,d largest eigenvalues of A where it will run 10 iterations for each eigenvalues estimation. Use the initial vector, z^(0) = ones(k) where k is the dimension of A.

Explanation / Answer

reference links:

http://math.oregonstate.edu/~math_reu/proceedings/REU_Proceedings/Proceedings1993/1993MacLean.pdf

http://math.unice.fr/~frapetti/CorsoF/cours4part2.pdf

http://www.math.pitt.edu/~sussmanm/2071Spring09/lab08/

http://people.inf.ethz.ch/arbenz/ewp/Lnotes/chapter6.pdf

http://www.jmlr.org/papers/volume14/yuan13a/yuan13a.pdf

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