Preconditioning approaches related to canonical correlation by use of cyclic form

Authors:
Raimundo J. B. De Sampaioa;Wenyu Sun;Jin Yun Yuan
Affiliations:
Pontifical Catholic University of Parana, Graduate Program in Production and Systems Engineering, Curitiba, Parana, Brazil;School of Mathematics and Computer Science, Nanjing Normal University, Nanjing, China;Department of Mathematics, Federal University of Paraná, Curitiba, Parana, Brazil
Venue:
International Journal of Systems Science
Year:
2009

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Abstract

There are many situations in engineering where we need to calculate the eigensystem of a matrix A which is given as a product of matrices, that is, A = A1A2...Ap. Since, usually, we first perform the multiplication of the factors, the matrix A often becomes very ill-conditioned. Actually this happens even when A is a symmetric matrix, which will be our concern here. In this article we introduce a new approach to calculate the eigensystem of A without performing the indicated multiplication, or performing only partially the multiplication of the factors.