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1994 | OriginalPaper | Buchkapitel

Analysis for M-Matrices

verfasst von : Wolfgang Hackbusch

Erschienen in: Iterative Solution of Large Sparse Systems of Equations

Verlag: Springer New York

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The positive definiteness A > 0 establishes a partial-order relation in the algebra of the Hermitian matrices. Another order relation in the algebra of all real matrices is defined by elementwise inequalities: 6.1.1a$$ A\, > \,B\,: \Leftrightarrow \,{a_{\alpha \beta }}\, > \,{b_{\alpha \beta }}\,\,for\,all\,\alpha ,\,\beta \, \in \,I, $$6.1.1b$$ A\; \ge \;B: \Leftrightarrow {a_{\alpha \beta }}\; \ge \;{b_{\alpha \beta }}\;\;{\rm{for all }}\alpha {\rm{,}}\;\beta \; \in \;I. $$ In this chapter, we use the signs «>» and «≥» only in the componentwise sense (1a, b).

Metadaten
Titel
Analysis for M-Matrices
verfasst von
Wolfgang Hackbusch
Copyright-Jahr
1994
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4612-4288-8_6