Abstract
The power iteration is a classical method for computing the eigenvector associated with the largest eigenvalue of a matrix. The subspace iteration is an extension of the power iteration where the subspace spanned by n largest eigenvectors of a matrix, is determined. The natural power iteration is an exemplary instance of the subspace iteration, providing a general framework for many principal subspace algorithms. In this paper we present variations of the natural power iteration, where n largest eigenvectors of a symmetric matrix without rotation ambiguity are determined, whereas the subspace iteration or the natural power iteration finds an invariant subspace (consisting of rotated eigenvectors). The resulting method is referred to as constrained natural power iteration and its fixed point analysis is given. Numerical experiments confirm the validity of our algorithm.
An erratum to this chapter can be found at http://dx.doi.org/10.1007/11550907_163 .
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Choi, S. (2005). On Variations of Power Iteration. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds) Artificial Neural Networks: Formal Models and Their Applications – ICANN 2005. ICANN 2005. Lecture Notes in Computer Science, vol 3697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11550907_24
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DOI: https://doi.org/10.1007/11550907_24
Publisher Name: Springer, Berlin, Heidelberg
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