Linearizations, realization, and scalar products for regular matrix polynomials

✍ Scribed by Ilya Krupnik; Peter Lancaster

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 595 KB
• Volume: 272
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(97)00301-7

✦ Synopsis

The connections between linearizations of regular matrix polynomials ZJ h) under shift and inversion of the parameter are developed and used to obtain a new formula for the realization of L(A)-'. In the self-adjoint case nondegenerate indefinite scalar products are obtained in which the fundamental (companion) linearizations arc self-adjoint. 6 19% Elsevier Scienccx Inc. 1.

but det L(A) f 0, i.e. the regular case.

In this situation, it is natural to rely on a parameter "shift and invert" strategy to transform the regular matrix polynomial to one with an invertible leading coefficient.

Such a strategy is carefully developed here, beginning