On local quadratic convergence of inexact simplified Jacobi-Davidson method
On local quadratic convergence of inexact simplified Jacobi-Davidson method
复制标题
不精确简化Jacobi-Davidson方法的局部二次收敛
DOI：
10.1016/j.laa.2017.01.018
复制
发表时间：
2017
影响因子：
1.1
通讯作者：
Miao Cun-Qiang
中科院分区：
文献类型：
--
作者：
Bai Zhong-Zhi;Miao Cun-Qiang
对于Hermitian特征值问题，当松弛修正方程采用标准Krylov子空间迭代求解时，我们证明了非精确简化Jacobi-Davidson方法的局部二次收敛性.然后，当松弛的校正方程被求解到与当前残差的范数成比例的预定精度时，该方法显示局部三次收敛速度。作为一个副产品，我们得到了局部三次收敛的简化Jacobi-Davidson方法。这些结果显着改善了现有的只显示局部线性收敛的不精确简化Jacobi-Davidson方法，这导致局部二次收敛的简化Jacobi-Davidson方法时，不精确的解决方案的公差特别是设置为零。数值实验证实了这些理论结果。
For the Hermitian eigenproblems, we prove local quadratic convergence of the inexact simplified Jacobi–Davidson method when the involved relaxed correction equation is solved by a standard Krylov subspace iteration. This method then shows local cubic convergence rate when the relaxed correction equation is solved to a prescribed precision proportional to the norm of the current residual. As a by-product, we obtain local cubic convergence of the simplified Jacobi–Davidson method. These results significantly improve the existing ones that show only local linear convergence for the inexact simplified Jacobi–Davidson method, which lead to local quadratic convergence for the simplified Jacobi–Davidson method when the tolerance of the inexact solve is particularly set to be zero. Numerical experiments confirm these theoretical results.