Priorconditioners for linear systems

被引:39
作者
Calvetti, D
Somersalo, E
机构
[1] Case Western Reserve Univ, Dept Math, Cleveland, OH 44106 USA
[2] Case Western Reserve Univ, Ctr Modeling Integrated Metab Syst, Cleveland, OH 44106 USA
[3] Aalto Univ, Inst Math, FIN-02015 Espoo, Finland
关键词
D O I
10.1088/0266-5611/21/4/014
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The construction of suitable preconditioners for the solution of linear systems by iterative methods continues to receive a lot of interest. Traditionally, preconditioners are designed to accelerate convergence of iterative methods to the solution of the linear system. However, when truncated iterative methods are used as regularized solvers of ill-posed problems, the rate of convergence is seldom an issue, and traditional preconditioners are of little use. Here, we present a new approach to the design of preconditioners for ill-posed linear systems, suitable when statistical information about the desired solution or a collection of typical solutions is available. The preconditioners are constructed from the covariance matrix of the solution viewed as a random variable. Since the construction is based on available prior information, these preconditioners are called priorconditioners. A statistical truncation index selection. is also presented. Computed examples illustrate how effective such priorconditioners can be.
引用
收藏
页码:1397 / 1418
页数:22
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