The adaptive augmented GMRES method for solving ill-posed problems
The adaptive augmented GMRES method for solving ill-posed problems
复制标题
解决不适定问题的自适应增强 GMRES 方法
DOI：
10.21914/anziamj.v50i0.1444
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发表时间：
2009
期刊：
影响因子：
0.9
通讯作者：
T. Nodera
中科院分区：
文献类型：
--
作者：
Nao Kuroiwa;T. Nodera
GMRES方法是一种迭代方法，在处理具有非对称系数矩阵的大型线性方程组时提供了更好的解。GMRES方法生成解的Krylov子空间，而增广GMRES方法允许通过用户提供的表示期望解的某些已知特征的子空间来扩展Krylov子空间。增广GMRES方法在适当的增广情况下表现良好，但在不适当的增广时表现较差。自适应增广GMRES方法从用户提供的候选集合中自动选择合适的子空间。研究表明，该方法保持了增强型GMRES的性能水平，减轻了用户的负担。数值实验比较了各种启发式策略的稳健性和效率。
参考文献M.L.Baart.在噪声病态线性最小二乘问题中使用自相关确定伪秩值。《IMA数值分析杂志》，2：241--247,1982。DOI：10.1093/imanum/2.2.241 J.baglama and L.Reichel.增广GMRES类方法。《数值线性代数及其应用》，14：337--350,2007。DOI：10.1002/nla.518 D.Calvetti，B.Lewis和L.Reichel不一致系统的GMRES类方法。《线性代数及其应用》，316：157--169,2000。DOI：10.1016/S0024-3795(00)00064-1 D.Calvetti，B.Lewis和L.Reichel。关于线性离散不适定问题迭代方法的子空间的选择。内部J.Appl.数学课。电脑。SCI，11：1069--1092,2001。Http://www.math.kent.edu/Reichel/出版物/子空间选择.pdf G.H.戈卢布和C.F.Van Loan。矩阵计算。约翰·霍普金斯大学出版社，第2版，1989年。P.C.汉森。正则化工具：一个分析和解决离散不适定问题的MatLab程序包。数值算法，6：1--35,1994。DOI：10.1007/BF02149761P.C.Hansen.秩亏和离散不适定问题。暹罗，费城，1998。Y·萨阿德。和M.H.舒尔茨。GMRES：一种求解非对称线性方程组的广义最小残值法。暹罗·J·科学。统计一下。电脑。，7：856--869,1986。Http://www.stanford.edu/class/cme324/saad-schultz.pdf
The GMRES method is an iterative method that provides better solutions when dealing with large linear systems of equations with a non-symmetric coefficient matrix. The GMRES method generates a Krylov subspace for the solution, and the augmented GMRES method allows augmentation of the Krylov subspaces by a user supplied subspace which represents certain known features of the desired solution. The augmented GMRES method performs well with suitable augmentation, but performs poorly with unsuitable augmentation. The adaptive augmented GMRES method automatically selects a suitable subspace from a set of candidates supplied by the user. This study shows that this method maintains the performance level of augmented GMRES and lightens the burden it puts on its users. Numerical experiments compare robustness as well as the efficiency of various heuristic strategies.
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