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Convergence and comparison theorems for multisplittings

✍ Scribed by Joan-Josep Climent; Carmen Perea

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 80 KB
Volume: 6
Category: Article
ISSN: 1070-5325
DOI: 10.1002/(sici)1099-1506(199903)6:2<93::aid-nla149>3.0.co;2-8

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✦ Synopsis

To solve a linear system Ax = b by an iterative method, it is customary to use a splitting of A in the sequential case and a multisplitting of A in the parallel case. In both cases, the convergence of the method is given by the spectral radius of the correspondent iteration matrix. Using the splittings of the second type and establishing an alternative convergence result for weak splittings, we extend the convergence result of O' Leary and White (1985) and the comparison result of . Also, we introduce new convergence and comparison results for weak multisplittings. On the other hand, introducing the concept of weak nonnegative definite splitting we present new convergence and comparison results for positive definite matrices which extend the results of O' Leary and White (1985) and .

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