关于BML矩阵的一种快速Arnoldi方法
On a fast Arnoldi method for BML matrices
AI总结：
本文提出一种快速Arnoldi方法用于BML矩阵，通过GMRES残差向量生成正交Krylov基，利用低秩结构简化计算。
摘要：
adjoint是矩阵有理函数的低秩扰动的矩阵在扩展著名的Faber-Manteuffel定理时自然出现，该定理提供了短Arnoldi递推存在的必要和充分条件。我们展示该类矩阵的正交Krylov基可通过基于GMRES残差向量的短递推关系生成。这些残差向量通过更新公式计算。此外，底层的Hessenberg矩阵具有伴随的低秩结构，我们将深入探讨。
英文摘要：
Matrices whose adjoint is a low rank perturbation of a rational function of the matrix naturally arise when trying to extend the well known Faber-Manteuffel theorem, which provides necessary and sufficient conditions for the existence of a short Arnoldi recurrence. We show that an orthonormal Krylov basis for this class of matrices can be generated by a short recurrence relation based on GMRES residual vectors. These residual vectors are computed by means of an updating formula. Furthermore, the underlying Hessenberg matrix has an accompanying low rank structure, which we will investigate closely.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
