Accuracy Improvement of the Shifted Block BiCGGR Method for Linear Systems with Multiple Shifts and Multiple Right-Hand Sides
Accuracy Improvement of the Shifted Block BiCGGR Method for Linear Systems with Multiple Shifts and Multiple Right-Hand Sides
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DOI：
10.1007/978-3-319-62426-6_12
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发表时间：
2015-09
期刊：
影响因子：
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通讯作者：
Hiroto Tadano;S. Saito;A. Imakura
中科院分区：
文献类型：
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作者：
Hiroto Tadano;S. Saito;A. Imakura
我们考虑求解具有多个移位和多个右侧的线性系统。为了有效地求解这些线性系统，我们开发了 Shifted Block BiCGGR 方法。该方法基于块 Krylov 子空间的平移不变性。利用这一性质，可以在求解种子系统的过程中求解平移系统，而无需矩阵向量乘法。 Shifted Block BiCGGR 方法可以生成种子系统的高精度近似解。然而，由于算法中出现的矩阵乘法误差，Shifted系统的近似解的精度可能会下降。在本文中，我们提高了 Shifted Block BiCGGR 方法生成的 Shifted 系统近似解的精度。
We consider solving linear systems with multiple shifts and multiple right-hand sides. In order to solve these linear systems efficiently, we develop the Shifted Block BiCGGR method. This method is based on the shift-invariance property of Block Krylov subspaces. Using this property, the Shifted systems can be solved in the process of solving the Seed system without matrix-vector multiplications. The Shifted Block BiCGGR method can generate high accuracy approximate solutions of the Seed system. However, the accuracy of the approximate solutions of the Shifted systems may deteriorate due to the error of the matrix multiplications appearing in the algorithm. In this paper, we improve the accuracy of the approximate solutions of the Shifted systems generated by the Shifted Block BiCGGR method.