基于K-非负矩阵理论的并行多分裂法的比较定理（英文）
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摘要
研究了两个迭代矩阵渐近收敛速度的比较.基于K-非负矩阵理论,用于刻画两种并行多分裂迭代法收敛速度快慢的结论被推导出.具体数值例子表明本文所得结果正确有效.
The comparisons of asymptotic rates of convergence of two iteration matrices are investigated. On the basis of K-nonnegative matrix theory, comparisons between two parallel multisplitting methods are derived. Then numerical example is given to show the validity of the comparison results.
The comparisons of asymptotic rates of convergence of two iteration matrices are investigated. On the basis of K-nonnegative matrix theory, comparisons between two parallel multisplitting methods are derived. Then numerical example is given to show the validity of the comparison results.
引文
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4 Krein M G,Rutman M A.Linear operators leaving invariant a cone in a Banach space[J].Amer Math Soc Transl Ser I,1962,10:199-325,
5 Hou G L.Comparison theorems for double splittings of K-monotone matrices[J].Appl Math Comput,2014,244:382-389.
6 Hou G L,Li N.K-nonnegative matrices and comparison theorems for iterative methods based on splitting[J].Advances in Mathematics,2014,43:463-479.
7 Marek I,Szyld D B.Comparison theorems for weak splittings of bounded operators[J].Numer Math,1990,58:387-397.
8 Climent J J,Perea C.Comparison theorems for weak nonnegative splittings of K-monotone matrices[J].The Electronic Journal of Linear Algebra,1999,5:24-38.
2 Song Y.Comparison theorems for splittings of matrices[J].Numer Math,2002,92:563-591.
3 Berman A,Plemmons R J.Nonnegative Matrices in the Mathematical Sciences[M].New York:Academic Press,1979.
4 Krein M G,Rutman M A.Linear operators leaving invariant a cone in a Banach space[J].Amer Math Soc Transl Ser I,1962,10:199-325,
5 Hou G L.Comparison theorems for double splittings of K-monotone matrices[J].Appl Math Comput,2014,244:382-389.
6 Hou G L,Li N.K-nonnegative matrices and comparison theorems for iterative methods based on splitting[J].Advances in Mathematics,2014,43:463-479.
7 Marek I,Szyld D B.Comparison theorems for weak splittings of bounded operators[J].Numer Math,1990,58:387-397.
8 Climent J J,Perea C.Comparison theorems for weak nonnegative splittings of K-monotone matrices[J].The Electronic Journal of Linear Algebra,1999,5:24-38.