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Exercise 6.8 Use the result of Proposition 6.1 to find a suitable shift for the...

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Exercise 6.8 Use the result of Proposition 6.1 to find a suitable shift for the computation of the maximum modulus eigenvalue of A= 5 0 1 -1 0 2 0 0 1 - 1 1 -1 -1 0 0 Then compare the number of iterations as well the computational cost of the power method both with and without shift by setting the tolerance equal to 10-14 Proposition 6.1 All the eigenvalues of a given matrix Ae Cnxn belong to the region of the complex plane which is the intersection of the two regions formed respectively by the union of the row circles and column circles. Moreover, should m row circles (or column circles), with 1

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