On the closed representation for the inverses of Hessenberg matrices

[摘要] The general representation for the elements of the inverse of any Hessenberg matrix of finite order is here extended to the reduced case with a new proof. Those entries are given with proper Hessenbergians from the original matrix. It justifies both the use of linear recurrences of unbounded order for such computations on matrices of intermediate order, and some elementary properties of the inverse. These results are applied on the resolvent matrix associated to a finite Hessenberg matrix in standard form. Two examples on the unit disk are given. (C) 2011 Elsevier B.V. All rights reserved.

[发布日期] 2012-06-01

[效力级别]  Proceedings Paper

[关键词] General orthogonal polynomials;Hessenberg matrix;Hessenbergian;Inverse matrix;Lower semiseparable (plus diagonal) matrix;Resolvent matrix