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- W2023187101 abstract "Thus far for an n × n complex nonsingular matrix A, the symmetric successive overrelaxation (SSOR) majorizing operator has been used to establish convergence properties of the SSOR method mostly in the case where A is an H-matrix. In this paper we use (actually a similarity transformation of) the SSOR majorizer to investigate convergence properties of the block SSOR method when A is a block p-cyclic matrix. Let JA denote the block Jacobi method and let ν = ϱ(¦JA¦). We establish regions in the (ν, ω)-plane where ϱ(SωA) ⩽ ϱ(QωA) < ¦ω − 1¦ [⩽ ϱ(LωA)]. Here SωA is the block SSOR iteration operator associated with A, LωA is the block successive overrelaxation (SOR) iteration operator associated with A, and QωA is a convenient similarity transformation of the majorizing operator for SωA. Of special interest to us are the values of ν for which the above inequality holds for the corresponding values of the relaxation parameter ω(A) = 2(1 + ν), the latter being an important quantity in the SOR-SSOR theory for H-matrices." @default.
- W2023187101 created "2016-06-24" @default.
- W2023187101 creator A5019944397 @default.
- W2023187101 creator A5066064955 @default.
- W2023187101 date "1995-08-01" @default.
- W2023187101 modified "2023-09-27" @default.
- W2023187101 title "Superior convergence domains for the p-cyclic SSOR majorizer" @default.
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- W2023187101 doi "https://doi.org/10.1016/0377-0427(94)00098-1" @default.
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