積分方程保奇性多尺度快速Galerkin方法離散矩陣性態(tài)分析

陳 杰

（宜賓學(xué)院數(shù)學(xué)學(xué)院，四川宜賓 644000）

積分方程保奇性多尺度快速Galerkin方法離散矩陣性態(tài)分析

陳 杰

（宜賓學(xué)院數(shù)學(xué)學(xué)院，四川宜賓 644000）

針對采用保奇性方法求解具有非光滑解的積分方程時所得到的離散線性方程組，分析了該方程組系數(shù)矩陣的各種性態(tài)，包括元素值估計、分塊矩陣范數(shù)估計等，并最終得到了系數(shù)矩陣條件數(shù)的有界性估計．

積分方程；系數(shù)矩陣；范數(shù)；條件數(shù)

具有非光滑解的積分方程來自于許多實際物理問題,如位勢問題、Dirichlet問題以及輻射平衡的數(shù)學(xué)問題等[1-3]．對它的求解有乘積-積分法、Galerkin方法和配置法等，它們都需要針對解的特性來構(gòu)造網(wǎng)格剖分；而采用多尺度保奇性方法求解此類問題能夠保持解的物理特性，還能進行快速求解[4，5]，因此更貼近實際應(yīng)用．本文主要研究多尺度保奇性Galerkin方法求解此類問題時所得到的離散系數(shù)矩陣的性態(tài)，它對于最終如何求解此線性方程組有著重要的意義[6]．

1 保奇性Galerkin方法

2 多尺度小波基底

3 方程離散分塊格式

4 離散矩陣性態(tài)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

宜賓學(xué)院博士啟動基金項目（2010B08）．

陳杰（1982-），男，四川宜賓人，宜賓學(xué)院數(shù)學(xué)學(xué)院教師．

責(zé)任編輯 朱本華