论文标题
转基因收敛范围的描述性如何？
How Descriptive are GMRES Convergence Bounds?
论文作者
论文摘要
GMRES是一种流行的Krylov子空间方法，用于求解涉及一般非弱系数矩阵的方程式线性系统。转基因收敛的常规界限涉及复杂平面中的多项式近似问题。三种流行的方法在系数矩阵的频谱，值或伪谱上提出了这个近似问题。我们分析和比较这些界限，以六个示例说明了每个界限的成功和失败。当仅由于低维不变子空间而脱离正态性时，我们会讨论如何适应这些界限以利用这种结构。由于基于GMRE的Arnoldi过程提供了对伪谱的近似值，因此可以估计GMRE的收敛范围作为迭代进行。
GMRES is a popular Krylov subspace method for solving linear systems of equations involving a general non-Hermitian coefficient matrix. The conventional bounds on GMRES convergence involve polynomial approximation problems in the complex plane. Three popular approaches pose this approximation problem on the spectrum, the field of values, or pseudospectra of the coefficient matrix. We analyze and compare these bounds, illustrating with six examples the success and failure of each. When the matrix departs from normality due only to a low-dimensional invariant subspace, we discuss how these bounds can be adapted to exploit this structure. Since the Arnoldi process that underpins GMRES provides approximations to the pseudospectra, one can estimate the GMRES convergence bounds as an iteration proceeds.
