摘要
设Au=b是二阶椭圆方程的差分逼近,熟知矩阵A的条件数cond(A)=O(h ̄(-2))(h→0).将差分方程表为GDM(广义差分法)形式,并利用分层基法将它化为等价方程Bv=c,使cond(B)=O((Igh ̄(-1)) ̄2).然后用某些迭比法(包括Richardson迭氏、共轭斜量法和Chebyshv半迭代)解Bv=c。理论分析和数值试验证明有高敛速。
Let Au=b be the difference approximation to the second order elliptic equation. It is knownthat the conditional number of matrix A has the asymptotic relation cond(A)=O(h ̄(-2))as h→0.Inthis paper,we express the difference schemes as the form of GDM(generalized difference methods,cf.[2] ),and transfer it into an equivalent system Bv=by the hierachical basis methods[1] so that thecond(B)equalstoO((Igh ̄(-1)) ̄2).Finally,several iterated methods(including Richardson's iteration,conjugate gradient method and Chebyshev semi-iteration)are used to solve Bv=c,The higher conver-gence rate has been testified by the theoretical analysis and a numerical example.
出处
《吉林大学自然科学学报》
CAS
CSCD
1995年第1期9-13,共5页
Acta Scientiarum Naturalium Universitatis Jilinensis
基金
国家教委博士点基金
关键词
广义
分层基
条件数
迭代法
差分方程
generalized difference methods,hierarchical basis,conditional number,iterative method