论文标题
（翻转）toeplitz矩阵和相关计算建议的特征值，奇异值和特征向量的理论结果
Theoretical results for eigenvalues, singular values, and eigenvectors of (flipped) Toeplitz matrices and related computational proposals
论文作者
论文摘要
在最近的一系列论文中，矩阵序列$ \ {y_nt_n（f）\} $的光谱行为是从光谱分布的意义上进行研究的，其中$ y_n $是主要的抗抗体（或flip矩阵）和$ t_n（f）$是由Fore toeplitz matter and toeplitz metier and fore $ f $ f $ f $ f $ f $。系数。此类研究还以计算目的是使用（预处理的）微小算法来解决相关大型线性系统的动机。在这里，我们对光谱研究进行补充，并在渐近和固定尺寸$ n $方面保持更多结果，以及$ t_n（f），y_nt_n（f）$的特征值，奇异价值和特征向量，以及它们之间的几个关系：旁边的快速线性溶解器旁边的目标是与Ad hoctria a depract a a ad hoctria a a a d of a a d superctra a a a dectials a a a dectials a a a dectials a a a dectials a的设计。成本在计算的特征值数量中是线性的。我们强调的是，在当前的工作中考虑了非单调酮生成功能的挑战，而先前的无基质算法失败了。报告和评论数值实验，目的是以视觉方式显示理论分析。
In a series of recent papers the spectral behavior of the matrix sequence $\{Y_nT_n(f)\}$ is studied in the sense of the spectral distribution, where $Y_n$ is the main antidiagonal (or flip matrix) and $T_n(f)$ is the Toeplitz matrix generated by the function $f$, with $f$ being Lebesgue integrable and with real Fourier coefficients. This kind of study is also motivated by computational purposes for the solution of the related large linear systems using the (preconditioned) MINRES algorithm. Here we complement the spectral study with more results holding both asymptotically and for a fixed dimension $n$, and with regard to eigenvalues, singular values, and eigenvectors of $T_n(f), Y_nT_n(f)$ and to several relationships among them: beside fast linear solvers, a further target is the design of ad hoc procedures for the computation of the related spectra via matrix-less algorithms, with a cost being linear in the number of computed eigenvalues. We emphasize that the challenge of the case of non-monotone generating functions is considered in the current work, for which the previous matrix-less algorithms fail. Numerical experiments are reported and commented, with the aim of showing in a visual way the theoretical analysis.
