多右端线性方程组的收缩迭代法
Deflated Iterative Methods for Linear Equations with Multiple Right-Hand Sides
摘要：
讨论了求解具有多个右侧的大型非对称线性方程组的一种新方法。第一个系统是用一个放气的GMRES方法求解，该方法在求解线性方程组的同时生成特征向量信息。随后的系统解决了重新启动GMRES与先前确定的特征向量的投影。这种方法提供了块方法的替代方案，也可以与块方法结合使用。当有有限数量的小特征值会减慢收敛速度时，它很有用。最后给出了一个例子，说明对量子色动力学的一个问题的改进。第二个和随后的右手边比没有通货紧缩的情况下更快地解决。这种新方法相对简单，与其他放气方法相比非常有效。
英文摘要：
A new approach is discussed for solving large nonsymmetric systems of linear equations with multiple right-hand sides. The first system is solved with a deflated GMRES method that generates eigenvector information at the same time that the linear equations are solved. Subsequent systems are solved by combining restarted GMRES with a projection over the previously determined eigenvectors. This approach offers an alternative to block methods, and it can also be combined with a block method. It is useful when there are a limited number of small eigenvalues that slow the convergence. An example is given showing significant improvement for a problem from quantum chromodynamics. The second and subsequent right-hand sides are solved much quicker than without the deflation. This new approach is relatively simple to implement and is very efficient compared to other deflation methods.
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