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I know the Power methods and Jacobi methods are suitable to finding eigenvalues for symmetric matrices, please tell me other methods for this matrices. And what are the methods for the Non-symmetric eigenvalue problems? Thanks a lot.

user115927
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2 Answers2

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QR algorithm and Francis's algorithm are two different names for the same thing.

For symmetric matrices there is also the Jacobi Method. The Jacobi Method is both easy to code, and reasonably fast. It basically diagonalizes the 2 by 2 submatrices again and again, and by some amzing magic, the iterates converge to a diagonal matrix.

Stephen Montgomery-Smith
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Here is a list of algorithms I have used while I was a student:

  • Power's method.
  • QR algorithm.
  • Francis' algorithm.

Cheers!

Dmoreno
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  • Thanks.Are these methods for symmetric matrices? – user115927 Jan 31 '14 at 17:36
  • I do not rememeber well if Francis' algorithm suffered any restriction about this. But QR algorithm is suitable for symmetric and non-symmetric. We used to implement it using Householder reflections. Cheers! – Dmoreno Jan 31 '14 at 17:40