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Polynomial Preconditioned Arnoldi with Stability Control
SIAM Journal on Scientific Computing ( IF 3.1 ) Pub Date : 2021-01-04 , DOI: 10.1137/19m1302430
Mark Embree , Jennifer A. Loe , Ronald Morgan

SIAM Journal on Scientific Computing, Volume 43, Issue 1, Page A1-A25, January 2021.
Polynomial preconditioning can improve the convergence of the Arnoldi method for computing eigenvalues. Such preconditioning significantly reduces the cost of orthogonalization; for difficult problems, it can also reduce the number of matrix-vector products. Parallel computations can particularly benefit from the reduction of communication-intensive operations. The GMRES algorithm provides a simple and effective way of generating the preconditioning polynomial. For some problems high degree polynomials are especially effective, but they can lead to stability problems that must be mitigated. A two-level “double polynomial preconditioning” strategy provides an effective way to generate high-degree preconditioners.


中文翻译:

具有稳定性控制的多项式预处理Arnoldi

SIAM科学计算杂志,第43卷,第1期,第A1-A25页,2021年1月。
多项式预处理可以改善Arnoldi方法用于计算特征值的收敛性。这种预处理大大降低了正交化的成本;对于棘手的问题,它还可以减少矩阵向量乘积的数量。并行计算可以从减少通信密集型操作中特别受益。GMRES算法为生成预处理多项式提供了一种简单有效的方法。对于某些问题,高阶多项式特别有效,但它们会导致必须解决的稳定性问题。二级“双多项式预处理”策略提供了一种生成高级预处理器的有效方法。
更新日期:2021-01-05
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