Data Science: Computation of Eigenvectors — QR-Algorithm.
This story is part of my Data Science series.
After having seen various methods about eigenvector computation, i.e. power method and deflation method, we now come to one that is hard to surpass in terms of ingenuity.
As common, the algorithm can be best understood by first looking at its theoretical background.
QR-algorithm:
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.
