Matlab Help

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]

[Geoff]

So... do they TEACH MatLab in this course you're doing? Or is the course all about finding other people who know MatLab and asking them to do assignments for you?

Nice tags, Walter =)

[Walter Roberson]

Are you sure you want to order all of the MATLAB Answers users to solve the same problem? Do you have the resources to sort through all 36000 individual answers?

[Richard Brown]

While we're at it, the question is malformed.

A diagonalisable matrix does not necessarily have a strictly dominant eigenvalue, nor, even if it does have one, will it appear in the first position of D if you arrange the eigenvalues of A in decreasing order.

That it has a strictly dominant eigenvalue (not defined here) is an assumption, and the ordering of D in the exposition at the start should be decreasing by *absolute* value.

That said, the algorithm presentation at least will work. Just do that.

[Walter Roberson]

I seem to be having difficulty in distinguishing between ones and ells ?

[Richard Brown]

lol. I wonder how much longer this question will last

Answer 1

[Richard Brown]

"Use MATLAB to solve the following...."

I've done it, now what do I get? Chocolate fish?