Dissecting the FEAST algorithm for generalized eigenproblems

We analyze the FEAST method for computing selected eigenvalues and eigenvectors of large sparse matrix pencils. After establishing the close connection between FEAST and the well-known Rayleigh-Ritz method, we identify several critical issues that influence convergence and accuracy of the solver: the choice of the starting vector space, the stopping criterion, how the inner linear systems impact the quality of the solution, and the use of FEAST for computing eigenpairs from multiple intervals. We complement the study with numerical examples, and hint at possible improvements to overcome the existing problems.Comment: 11 Pages, 5 Figures. Submitted to Journal of Computational and Applied Mathematic

Zolotarev Quadrature Rules and Load Balancing for the FEAST Eigensolver

The FEAST method for solving large sparse eigenproblems is equivalent to subspace iteration with an approximate spectral projector and implicit orthogonalization. This relation allows to characterize the convergence of this method in terms of the error of a certain rational approximant to an indicator function. We propose improved rational approximants leading to FEAST variants with faster convergence, in particular, when using rational approximants based on the work of Zolotarev. Numerical experiments demonstrate the possible computational savings especially for pencils whose eigenvalues are not well separated and when the dimension of the search space is only slightly larger than the number of wanted eigenvalues. The new approach improves both convergence robustness and load balancing when FEAST runs on multiple search intervals in parallel.Comment: 22 pages, 8 figure

Advances in Evolutionary Algorithms

With the recent trends towards massive data sets and significant computational power, combined with evolutionary algorithmic advances evolutionary computation is becoming much more relevant to practice. Aim of the book is to present recent improvements, innovative ideas and concepts in a part of a huge EA field

平成20年度 計算科学研究センター研究報告

1-1 素粒子分野1-2 宇宙分野2-1 計算物性分野2-2 原子核理論分野2-3 計算生命分野3-1 地球環境分野3-2 生物分野4-1 計算機アーキテクチャ研究分野5-1 計算知能分野5-2 計算メディア分