一类弱非线性方程组的Picard-MHSS迭代方法
ON PICARD-MHSS METHODS FOR WEAKLY NONLINEAR SYSTEMS
查看参考文献17篇
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文摘
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修正的Hermite/反Hermite分裂(MHSS)迭代方法是一类求解大型稀疏复对称线性代数方程组的无条件收敛的迭代算法.基于非线性代数方程组的特殊结构和性质,我们选取Picard迭代为外迭代方法,MHSS迭代作为内迭代方法,构造了求解大型稀疏弱非线性代数方程组的 Picard-MHSS和非线性MHSS-like方法.这两类方法的优点是不需要在每次迭代时均精确计算和存储Jacobi矩阵,仅需要在迭代过程中求解两个常系数实对称正定子线性方程组.除此之外,在一定条件下,给出了两类方法的局部收敛性定理.数值结果证明了这两类方法是可行、有效和稳健的. |
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其他语种文摘
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Modified Hermitian and skew-Hermitian splitting(MHSS) iteration method is an un? conditionally convergent method for solving large sparse complex symmetric linear systems. Based on the special structure and properties of the nonlinear systems, choosing Picard it? eration as outer iteration and MHSS iteration as the inner solver of Picard iteration, we present the Picard-MHSS and nonlinear MHSS-like iteration methods for solving large s- cale systems of weakly nonlinear equations. The advantage of these methods is that they do not require explicit construction and accurate computation of the Jacobian matrix, and only need to solve linear sub-systems of constant coefficient real symmetric positive definite matrices. Moreover, Under suitable conditions, we establish local convergence theorems for both Picar-MHSS and nonlinear MHSS-like iteration methods. Numerical results show that these iteration methods are feasible, effective and robust. |
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来源
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计算数学
,2014,36(3):291-302 【核心库】
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关键词
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非线性方程组
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Hermite反Hermite分裂
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Picard方法
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局部收敛性质
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地址
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1.
吉林师范大学数学学院, 吉林, 四平, 136000
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兰州大学数学与统计学院, 兰州, 730000
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语种
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中文 |
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文献类型
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研究性论文 |
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ISSN
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0254-7791 |
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学科
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数学;力学 |
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基金
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国家973计划
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吉林省自然科学基金
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吉林省教育厅十二五科技项目
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吉林师范大学博士启动项目资助
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吉林省四平市科技发展计划项目
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吉林师范大学研究生创新项目
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吉林师范大学高等教育教学研究项目
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吉林省科技发展计划项目
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吉林省四平市科技发展计划项目
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文献收藏号
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CSCD:5226740
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