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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/1445

Title: A Comparison of the Implicit Determinant Method and Inverse Iteration
Authors: Akinola, R. O.
Spence, A.
Keywords: quadratic convergence
Jordan blocks
AMS subject classification
Issue Date: 2014
Publisher: Journal of Nigerian Mathematical Society
Series/Report no.: Vol. 33;Pp 205-230
Abstract: It is well known that if the largest or smallest eigenvalue of a matrix has been computed by some numerical algorithms and one is interested in computing the correspond- ing eigenvector, one ‘method that is known to give such good approximations to the eigenvector is inverse iteration with a shift. However, in a situation where the desired eigenvalue is defective, inverse iteration converges harmonically to the eigen-value close to the shift. In this paper, we extend the implicit determinant method of Spence and Poulton [13] to compute a defective eigenvalue given a shift close to the eigenvalue of interest. For a defective eigenvalue, the proposed approach gives quadratic convergence and this is verified by some numerical experiments.
URI: http://hdl.handle.net/123456789/1445
Appears in Collections:Mathematics

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