LectureNotes 2006
نویسنده
چکیده
In this part, we discuss some practical methods for computing eigenvalues and eigenvectors of matrices. Needless to say, we completely avoid trying to solve (or even write down) the characteristic polynomial equation. The very basic power method and its variants, which is based on linear iteration, is used to effectively approximate selected eigenvalues. To determine the complete system of eigenvalues and eigenvectors, the remarkable QR algorithm, which relies on the Gram–Schmidt orthogonalization procedure, is the method of choice, and we shall close with a new proof of its convergence.
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