%0 Conference Paper
%B International Parallel and Distributed Processing Symposium (IPDPS)
%D 2019
%T Matrix Powers Kernels for Thick-Restart Lanczos with Explicit External Deflation
%A Zhaojun Bai
%A Jack Dongarra
%A Ding Lu
%A Ichitaro Yamazaki
%X Some scientific and engineering applications need to compute a large number of eigenpairs of a large Hermitian matrix. Though the Lanczos method is effective for computing a few eigenvalues, it can be expensive for computing a large number of eigenpairs (e.g., in terms of computation and communication). To improve the performance of the method, in this paper, we study an s-step variant of thick-restart Lanczos (TRLan) combined with an explicit external deflation (EED). The s-step method generates a set of s basis vectors at a time and reduces the communication costs of generating the basis vectors. We then design a specialized matrix powers kernel (MPK) that reduces both the communication and computational costs by taking advantage of the special properties of the deflation matrix. We conducted numerical experiments of the new TRLan eigensolver using synthetic matrices and matrices from electronic structure calculations. The performance results on the Cori supercomputer at the National Energy Research Scientific Computing Center (NERSC) demonstrate the potential of the specialized MPK to significantly reduce the execution time of the TRLan eigensolver. The speedups of up to 3.1× and 5.3× were obtained in our sequential and parallel runs, respectively.
%B International Parallel and Distributed Processing Symposium (IPDPS)
%I IEEE
%C Rio de Janeiro, Brazil
%8 2019-05
%G eng
%0 Book Section
%B Handbook of Linear Algebra
%D 2013
%T LAPACK
%A Zhaojun Bai
%A James Demmel
%A Jack Dongarra
%A Julien Langou
%A Jenny Wang
%X With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters.
%B Handbook of Linear Algebra
%7 Second
%I CRC Press
%C Boca Raton, FL
%@ 9781466507289
%G eng
%0 Journal Article
%J Philadelphia: Society for Industrial and Applied Mathematics
%D 1999
%T LAPACK Users' Guide, 3rd ed.
%A Ed Anderson
%A Zhaojun Bai
%A Christian Bischof
%A Susan Blackford
%A James Demmel
%A Jack Dongarra
%A Jeremy Du Croz
%A Anne Greenbaum
%A Sven Hammarling
%A Alan McKenney
%A Danny Sorensen
%B Philadelphia: Society for Industrial and Applied Mathematics
%8 1999-01
%G eng