Suppose we've found the dominant e.value & corresponding e.vector by power method and Rayleigh quotient. Then what about the others?!
We outline five such iterative methods to find all the eigenvalues & eigenvectors
the power iteration method, the shifted inverse iteration
method, the Rayleigh quotient method, the simultaneous iteration method, and the QR method.
My sincere gratitudes; dr.zarnan.
But 2 points i wanna mention here if i may.
First, the power method only gives the dominant eigenvector (and then eigenvalue)
And second, the QR factorization method hasn't iterative nature which is proper and optimal for coding.
And I don't have any idea about "shifted inverse iteration" and "simultaneous iteration" methods!
I will be indebted if you introduce me articles or some guidelines about the material.
Thanks a lot
There is a program source code to calculate the singular value decomposition (SVD) using Householder transformations in this archive http://dudleybenton.altervista.org/software/Orthogonal%20Functions/orthogonal_function_examples.zip in the folder examples/SVD called SVDtest.c You can get the book from Amazon for free today (11/26) or on 12/5, 12/13, 12/21, and 12/29 https://www.amazon.com/dp/B07GT8TLDV
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