Numerical Analysis/Inverse iteration exercises
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Consider the matrix, , and the vector,
The LU decomposition of A is .
By hand, use the LU decomposition to do two iterations of the inverse power method (without shift) starting with
Solution, first iteration:
. The estimated eigenvalue is and the estimated eigenvector is .
Solution, second iteration:
. The estimated eigenvalue is and the estimated eigenvector is .
Use a computational software package to do 50 iterations. What was the result?
Solution, 50 iterations:
The estimated eigenvalue after 50 iterations is and the estimated eigenvector is .