M-Matrices and Generalizations Using an Operator Theory Approach

M-Matrices and Generalizations Using an Operator Theory Approach

A theory on M-matrices is derived from simple results on inverse-positive linear operators. Some applications to eigenvalue theory and iterative procedures are discussed. The concepts occurring in this theory can be generalized. In particular, M-operators are introduced, which share many properties...

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Veröffentlicht in:SIAM review 1978-04, Vol.20 (2), p.213-244
1. Verfasser: Schroder, Johann
Format: Artikel
Sprache:eng
Schlagworte:
Eigenvalues
Linear algebra
Linear transformations
Mathematical inequalities
Mathematical procedures
Mathematical theorems
Mathematical vectors
Matrices
Perceptron convergence procedure
Theorems
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Zusammenfassung:A theory on M-matrices is derived from simple results on inverse-positive linear operators. Some applications to eigenvalue theory and iterative procedures are discussed. The concepts occurring in this theory can be generalized. In particular, M-operators are introduced, which share many properties with M-matrices. As special examples, certain boundary value problems are considered.
ISSN:0036-1445
1095-7200
DOI:10.1137/1020037