积分方程保奇性多尺度快速Galerkin方法离散矩阵性态分析

陈 杰

（宜宾学院数学学院，四川宜宾 644000）

积分方程保奇性多尺度快速Galerkin方法离散矩阵性态分析

陈 杰

（宜宾学院数学学院，四川宜宾 644000）

针对采用保奇性方法求解具有非光滑解的积分方程时所得到的离散线性方程组，分析了该方程组系数矩阵的各种性态，包括元素值估计、分块矩阵范数估计等，并最终得到了系数矩阵条件数的有界性估计．

积分方程；系数矩阵；范数；条件数

具有非光滑解的积分方程来自于许多实际物理问题,如位势问题、Dirichlet问题以及辐射平衡的数学问题等[1-3]．对它的求解有乘积-积分法、Galerkin方法和配置法等，它们都需要针对解的特性来构造网格剖分；而采用多尺度保奇性方法求解此类问题能够保持解的物理特性，还能进行快速求解[4，5]，因此更贴近实际应用．本文主要研究多尺度保奇性Galerkin方法求解此类问题时所得到的离散系数矩阵的性态，它对于最终如何求解此线性方程组有着重要的意义[6]．

1 保奇性Galerkin方法

2 多尺度小波基底

3 方程离散分块格式

4 离散矩阵性态分析

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Analysis of the Discrete Matrix Derived from the Fast Singularity Preserving Multilevel Galerkin Methods

CHEN Jie
（Department of Mathematics,Yibin University,Yibin 644000,China）

It is important to analyse the discrete matrix derived from the singularity preserving multilevel Galerkin methods.We need to estimate the value of elements,norm of the block matrices and the condition number of the coefficient matrix and so on.In the end,we obtain the boundness of the condition number controlled by a more simple matrix which is the key to solve the discrete equations.

integral equations；coefficient matrix；norm；condition number

A

1007-6883(2011)06-0012-05

2011-09-26

宜宾学院博士启动基金项目（2010B08）．

陈杰（1982-），男，四川宜宾人，宜宾学院数学学院教师．

责任编辑 朱本华