Data Science: Computation of Eigenvectors — QR-Algorithm.
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As common, the algorithm can be best understood by first looking at its theoretical background.
The power method, although applicable to a wide range of endomorphisms, has the drawback of computing only one eigenvector, i.e. the one with highest eigenvalue in absolute terms. Although, a deflation method can be applied to obtain all the eigenvectors one after the other, the numerical effort and in particular error can become a problem for very large systems. The following algorithm intends to solve this problem by providing an iterative method to obtain all eigenvector/eigenvalue pairs in one go.