摘要
应用改进的不完全双曲Gram-Schmidt(IHMGS)方法预处理不定最小二乘问题的共轭梯度法(CGILS)、正交分解法(ILSQR)与广义的最小剩余法(GMRES)等迭代算法来求解大型稀疏的不定最小二乘问题.数值实验表明,IHMGS预处理方法可有效提高相应算法的迭代速度,且当矩阵的条件数比较大时,效果更加显著.
Some iterative methods such as the conjugate gradient method for the indefinite least square problems(CGILSs),the sparse linear equations and indefinite least square problems(ILSQRs),and the generalized minimal residual(GMRES) method are preconditioned by the incomplete hyperbolic modified GramSchmidt (IHMGS) for the solution of the large and sparse indefinite least square problem.Numerical experiments show that the IHMGS preconditioner can greatly improve the iterative speed,especially for large-scale and ill-conditioned problems.
出处
《应用数学与计算数学学报》
2012年第1期45-52,共8页
Communication on Applied Mathematics and Computation
基金
国家自然科学基金资助项目(11001167)
上海市重点学科建设资助项目(J50101)
