ABSTRACT
Some important applicative problems require the evaluation of functions Ψ of large and sparse and/or localized matrices A. Popular and interesting techniques for computing and , where is a vector, are based on partial fraction expansions. However, some of these techniques require solving several linear systems whose matrices differ from A by a complex multiple of the identity matrix I for computing or require inverting sequences of matrices with the same characteristics for computing . Here we study the use and the convergence of a recent technique for generating sequences of incomplete factorizations of matrices in order to face with both these issues. The solution of the sequences of linear systems and approximate matrix inversions above can be computed efficiently provided that shows certain decay properties. These strategies have good parallel potentialities. Our claims are confirmed by numerical tests.
Acknowledgments
We wish to thank two anonymous referees for their constructive comments which have improved the readability of the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.