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Shawn
Shawn 2012-5-2
Use MATLAB to solve the following.
Assume that A is a diagonalizable matrix and that the diagonal matrix D related to A by D = P^-1 AP is such that its diagonal entries are arranged in decreasing order.
The value lambda 1 is called strictly dominant eigenvalue. Then the following method, called the Power Method, can be used to estimate the strictly dominant eigenvalue:
(1.1) Select an initial vector x0 whose largest entry is 1.
(1.2) For k = 0,1,2,... compute Axk. To calculate xk+1, let uk be an entry in Axk with largest absolute value, and then set xk+1 = (1/uk)Axk.
(1.3) For almost all choices of the initial vector, the sequence {uk} approaches the strictly dominant eigenvalue, while the sequence {xk} approaches a corresponding eigenvector.
(a) Use the power method to find an approximation of the strictly dominant eigenvalue and a corresponding eigenvector for the following data. Use 15 iterations.
(a1) A = [-4,-1,0; 0,-2,4; 2,0,1], x0 = [0;1;1]
(a2) A = [2,0,1;0,-2,4; 4,1,0], x0 = [0;1;1]
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Walter Roberson
Walter Roberson 2012-5-2
I seem to be having difficulty in distinguishing between ones and ells ?
Richard Brown
Richard Brown 2012-5-3
lol. I wonder how much longer this question will last

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Richard Brown
Richard Brown 2012-5-2
"Use MATLAB to solve the following...."
I've done it, now what do I get? Chocolate fish?

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