On the closed representation for the inverses of Hessenberg matrices

被引：13

作者：

Abderraman Marrero, J. ^{[2
]}

Tomeo, V. ^{[1
]}

机构：

[1] EUE UCM Univ Complutense, Dept Algebra, Sch Stat, Madrid 28040, Spain

[2] ETSIT UPM Madrid Tech Univ, Dept Math Appl Informat Technol, Telecommun Engn Sch, Madrid 28040, Spain

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2012年 / 236卷 / 12期

关键词：

General orthogonal polynomials; Hessenberg matrix; Hessenbergian; Inverse matrix; Lower semiseparable (plus diagonal) matrix; Resolvent matrix; VARIABLE-COEFFICIENTS; DIFFERENCE EQUATION; ALGORITHM;

D O I：

10.1016/j.cam.2011.07.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：2962 / 2970

页数：9

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