一种新的消去块GCROT($m,k$)方法用于求解具有多个右端向量的线性系统
A new deflated block GCROT($m,k$) method for the solution of linear systems with multiple right-hand sides
AI总结：
本文提出一种新的消去块GCROT($m,k$)方法，通过改进的块Arnoldi消去策略高效求解多右端向量线性系统，提升计算效率并避免冗余运算。
摘要：
具有多个右端向量的线性系统在许多应用中出现。为高效求解此类系统，本文探讨了一种新的消去块GCROT($m,k$)方法，通过利用改进的块Arnoldi消去策略。该消去策略已被证明能提升原始消去效果，表明显式块大小缩减的潜力。结合该改进的块Arnoldi消去，新算法可在每次块Arnoldi过程中处理可能的线性相关性，并避免昂贵的计算操作。此外，我们分析了其主要数学性质，并证明消去过程基于真实块残差奇异值的非递增行为。作为GCROT($m,k$)的块版本，新方法继承了易于操作的特性。最后，一些数值示例也展示了所提方法的有效性。
英文摘要：
Linear systems with multiple right-hand sides arise in many applications. To solve such systems efficiently, a new deflated block GCROT($m,k$) method is explored in this paper by exploiting a modified block Arnoldi deflation. This deflation strategy has been shown to have the potential to improve the original deflation which indicates an explicit block size reduction. Incorporating this modified block Arnoldi deflation, the new algorithm can address the possible linear dependence at each iteration during the block Arnoldi procedure and avoids expensive computational operations. In addition, we analyze its main mathematical properties and prove that the deflation procedure is based on a non-increasing behavior of the singular values of the true block residual. Moreover, as a block version of GCROT($m,k$), the new method inherits the property of easy operability. Finally, some numerical examples also illustrate the effectiveness of the proposed method.
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