Comparison theorems using general cones for norms of iteration matrices

We prove comparison theorems for norms of iteration matrices in splittings of matrices in the setting of proper cones in a finite dimensional real space by considering cone linear absolute norms and cone max norms. Subject to mild additional hypotheses, we show that these comparison theorems can hol...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 399; pp. 169 - 186
Main Authors Seidman, Thomas I., Schneider, Hans, Arav, Marina
Format Journal Article Conference Proceeding
LanguageEnglish
Published New York, NY Elsevier Inc 01.04.2005
Elsevier Science
Subjects
Algebra
Convex cone
Exact sciences and technology
Inequalities
Linear and multilinear algebra, matrix theory
Mathematics
Matrix norms
Positivity
Sciences and techniques of general use
Spectral radius
Splitting
15A42
Splitting
Matrix norms
Spectral radius
Positivity
Inequalities
15A48
15A60
Convex cone
15A18
Cone
Perron value
Normed space
15A15
Banach algebra
15A60 Convex cone
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Summary:We prove comparison theorems for norms of iteration matrices in splittings of matrices in the setting of proper cones in a finite dimensional real space by considering cone linear absolute norms and cone max norms. Subject to mild additional hypotheses, we show that these comparison theorems can hold only for such norms within the class of cone absolute norms. Finally, in a Banach algebra setting, we prove a comparison theorem for spectral radii without appealing to Perron–Frobenius theory.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2004.09.002