Convergence and comparison theorems for multisplittings (Q2760343)
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scientific article; zbMATH DE number 1684502
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convergence and comparison theorems for multisplittings |
scientific article; zbMATH DE number 1684502 |
Statements
19 December 2001
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nonnegative (multi) splitting
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positive definite (multi) splitting
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comparison conditions
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Convergence and comparison theorems for multisplittings (English)
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The authors extend \textit{D. P. O'Leary}'s and \textit{R. E. White}'s convergence results [SIAM J. Algebraic Discrete Methods 6, 630-640 (1985; Zbl 0852.65018)] and \textit{L. Elsner}'s comparison result [Numer. Math. 56, No. 2/3, 283-289 (1989; Zbl 0652.65024)] by using the splittings of the second type and establishing an alternative convergence result for weak splittings. There new convergence and comparison results for weak multisplitting were studied. They present new convergence and comparison results for positive definite matrices by introducing the concept of weak negative splitting, which also extend the results of D. P. O'Leary and R. E. White and \textit{R. Nabben} [Linear Algebra Appl. 233, 67-80 (1996; Zbl 0841.65019)].
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