发表机构
School of Mathematics, Trinity College Dublin（都柏林三一学院数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用Greenbaum-Strakoš理论，研究非Hermitian三对角Toeplitz矩阵上GMRES的可容许行为，证明Toeplitz结构约束了理论体现，但仍存在连续统的可达到行为。
AI 中文摘要
Greenbaum和Strakoš的结果表明，对于给定的特征值集合，任何收敛曲线都是可能的[SIMAX 1996]，随后Arioli、Pták和Strakoš[BIT 1998]对此类矩阵-右端向量对$(A,\mathbf{b})$的参数化表明，\gmres的行为不能仅由$A$的特征值完全刻画。在本文中，我们考虑如何利用这一理论来理解具有约束结构的矩阵的可容许和可达到的\gmres行为，重点关注非Hermitian（非对称）三对角Toeplitz矩阵。我们证明Toeplitz结构必然约束了这些论文中的理论如何体现，但连续统的可容许行为仍然可以达到。
英文摘要
The result of Greenbaum, Pták, and Strakoš that for a given set of eigenvalues, any convergence curve is possible [SIMAX 1996] and the subsequent parameterization of such matrix-right-hand side pairs $(A,\mathbf{b})$ of Arioli, Pták, and Strakoš [BIT 1998] demonstrated that the behavior of the \gmres could not be completely characterized by the eigenvalues of $A$ alone. In this paper, we consider how to use this theory to understand the admissible and attainable \gmres behavior for matrices with constrained structure, focussing on non-Hermitian (non-symmetric) tridiagonal Toeplitz matrices. We show that Toeptliz structure necessarily constrains the how the theory from these papers can manifest but that a continuum of admissible behaviors is still attainable.
Comments28 pages main text, 8 pages appendix text
