Preconditioning approaches related to canonical correlation by use of cyclic form

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 = A ₁ A ₂···A _p . 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.

Keywords:

• canonical correlation
• preconditioning
• eigensystem
• production engineering

Acknowledgements

We thank the Editor-in-Chief, the Associate Editor and two anonymous referees for their careful reading and helpful comments and suggestions which greatly improved our manuscript. This work was partially supported by CNPq Brazil and the National Natural Science Foundation of China No. 10871098.