【摘要】 基于投影方法的规划算法——Krylov子空间技术,研究了离散不适定正则化和Krylov子空间广义极小残余算法(GMRES(m))的基本理论,特别是残余向量与Krylov子空间的关系。利用离散不适定正则化方法,将不适定问题转化为适定问题,利用广义极小残余算法对此适定问题进行数值求解。数值结果表明该算法是可靠和有效的。更多还原

【Abstract】 This paper studies the fundamental theory of the discrete ill-posed regularization and the generalized minimal residual algorithm (GMRES(m)) based on Krylov subspace methods and specially the relationship between residual vector and Krylov subspace. The techniques are based on the projection process. Discrete ill-posed regularization methods convert ill-posed problems into posed problems, so the generalized minimal residual algorithm can be used in this kind of ill-posed problems. Numerical results show the reliability and efficiency of the algorithm.更多还原