On the closed representation for the inverses of Hessenberg matrices

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• 作者：J. Abderramá ; n Marrero^a ; ¹ ; ^{jc.abderraman@upm.es} ; V. Tomeo^b ; ^{tomeo@estad.ucm.es}
• 关键词：11B83 ; 15A09 ; 15A15 ; 33C45 ; 47A10 ; 65F05
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2012
• 期刊代码：72_03770427
• 类别：cp
• 出版时间：June, 2012
• 卷：236
• 期：12
• 页码：2962-2970
• 文件大小：252 K

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.