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Alternative correction equations in the Jacobi-Davidson method

✍ Scribed by Menno Genseberger; Gerard L. G. Sleijpen

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
114 KB
Volume
6
Category
Article
ISSN
1070-5325

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✦ Synopsis

The correction equation in the Jacobi-Davidson method is effective in a subspace orthogonal to the current eigenvector approximation, whereas for the continuation of the process only vectors orthogonal to the search subspace are of importance. Such a vector is obtained by orthogonalizing the (approximate) solution of the correction equation against the search subspace. As an alternative, a variant of the correction equation can be formulated that is restricted to the subspace orthogonal to the current search subspace. In this paper, we discuss the effectiveness of this variant.

Our investigation is also motivated by the fact that the restricted correction equation can be used for avoiding stagnation in the case of defective eigenvalues. Moreover, this equation plays a key role in the inexact TRQ method [18].

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