Polynomial Preconditioned Arnoldi
Polynomial Preconditioned Arnoldi
复制标题
多项式预条件 Arnoldi
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
R. Morgan
中科院分区：
文献类型：
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作者：
M. Embree;J. Loe;R. Morgan
多项式预处理可以提高Arnoldi方法计算特征值的收敛性。这种预处理显著降低了正交化的成本；对于困难的问题，它也可以减少矩阵-向量乘积的数量。并行计算尤其可以从减少通信密集型操作中获益。GMRES算法提供了一种简单有效的预处理多项式生成方法。对于某些问题，高次多项式是特别有效的，但它们可能导致稳定性问题，必须加以缓解。两级“双多项式预处理”策略为生成高阶预处理提供了有效的方法。
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.