Conference Paper

Inverses of regular Hessenberg matrices

June 2010

Conference: 10th International Conference on Computational and Mathematical Methods in Science and Engineering
Volume: 1

Authors:

Jesús Abderramán Marrero

Universidad Politécnica de Madrid

Complutense University of Madrid

A new proof of the general representation for the entries of the inverse of any unreduced Hessenberg matrix of finite order is found. Also this formulation is extended to the inverses of reduced Hessenberg matrices. Those matrices are given with proper Hessenbergians from the original matrix. It justifies both the use of linear recurrences for such computations and some elementary properties of the inverse matrix. As an application of current interest in the theory of orthogonal polynomials on the complex plane, the resolvent matrix associate to a finite Hessenberg matrix in standard form is calculated. THe results are illustrated with two examples on the unit disk.

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