Cao, Wei-Lu; Stewart, William J. A note on inverses of Hessenberg-like matrices. (English) Zbl 0617.65018 Linear Algebra Appl. 76, 233-240 (1986). Authors’ summary: We generalize some results of Y. Ikebe [ibid. 24, 93-97 (1979; Zbl 0397.15005)] concerning the inverse of an upper Hessenberg matrix. Specifically we prove a theorem to show that if A is a nonsingular block lower s-diagonal matrix (i.e. the blocks \(A_{ij}\) of A satisfy \(A_{ij}=0\) if \(i>j+s)\) and the blocks \(A_{j+s,j}\) are nonsingular, then the inverse of A may be written as \(A^{-1}=XY+Z\). The procedure for the computation of X, Y and Z as developed in the proof of this theorem lays the basis for an efficient implementation of the method on a parallel computer. Reviewer: F.Szidarovszky Cited in 2 Documents MSC: 65F05 Direct numerical methods for linear systems and matrix inversion 65Y05 Parallel numerical computation Keywords:inverse of an upper Hessenberg matrix; block lower s-diagonal matrix Citations:Zbl 0397.15005 PDFBibTeX XMLCite \textit{W.-L. Cao} and \textit{W. J. Stewart}, Linear Algebra Appl. 76, 233--240 (1986; Zbl 0617.65018) Full Text: DOI References: [1] Ikebe, Yashuhiko, On inverse of Hessenberg matrices, Linear Algebra Appl., 24, 93-97 (1979) · Zbl 0397.15005 [2] Gantmacher, F. R.; Krein, M. G., (Oszillationsmatrizen (1960), Akademie: Akademie Berlin), 95 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.