论文标题
块滤波器和本素溶剂的多数化型群集稳健界限
Majorization-type cluster robust bounds for block filters and eigensolvers
论文作者
论文摘要
对遗传学特征值问题的块迭代求解器的收敛分析以及基于基于矩阵的信号过滤器属性的密切相关的研究非常具有挑战性，并且由于其最近在频谱数据群集和基于图的信号处理中的应用而引起了越来越多的关注。我们结合了基于多数化的技术，用于研究[Siam J. Matrix肛门。 Appl。，31（2010），pp。1521-1537]，借助Rutishauser [Numer。 Math。，13（1969），pp。4-13]，得出抽象阻滞迭代的收敛速率界限，其中主角度的切线或丽思族的相对误差的元素是使用大量化的，以大量的分数为界面，以排列的部分总和和融合因子的分组。在存在特征值的簇的情况下，我们的新颖界限非常健壮，改善了一些先前的结果，并且适用于最著名的块基于迭代的求解器和基于矩阵的过滤器，例如阻止功率，Chebyshev和Lanczos方法，结合了转移和逆转方法和逆转方法和多态滤波。
Convergence analysis of block iterative solvers for Hermitian eigenvalue problems and the closely related research on properties of matrix-based signal filters are challenging, and attract increasing attention due to their recent applications in spectral data clustering and graph-based signal processing. We combine majorization-based techniques pioneered for investigating the Rayleigh-Ritz method in [SIAM J. Matrix Anal. Appl., 31 (2010), pp. 1521-1537] with tools of classical analysis of the block power method by Rutishauser [Numer. Math., 13 (1969), pp. 4-13] to derive convergence rate bounds of an abstract block iteration, wherein tuples of tangents of principal angles or relative errors of Ritz values are bounded using majorization in terms of arranged partial sums and tuples of convergence factors. Our novel bounds are robust in presence of clusters of eigenvalues, improve some previous results, and are applicable to most known block iterative solvers and matrix-based filters, e.g., to block power, Chebyshev, and Lanczos methods combined with shift-and-invert approaches and polynomial filtering.
