Computing humps of the matrix exponential

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:319

Article

Nechepurenko, Yu. M.¹  Sadkane, M.² 

[1] Russian Acad Sci, Inst Numer Math, Ul Gubkina 8, Moscow 119333, Russia

[2] Univ Brest, CNRS UMR 6205, Lab Math Bretagne Atlantique, CS 93837, 6 Ave Victor Le Gorgeu, F-29285 Brest 3, France

关键词: Matrix exponential norm;    Time integration method;    Krylov subspace method;    Truncated Taylor series method;    Lanczos method;    Alternating maximization;   

DOI  :  10.1016/j.cam.2016.12.031

来源: Elsevier

【 摘 要 】

This work is devoted to finding maxima of the function Gamma(t) = parallel to exp(tA) parallel to(2) where t >= 0 and A is a large sparse matrix whose eigenvalues have negative real parts but whose numerical range includes points with positive real parts. Four methods for computing Gamma(t) are considered which all use a special Lanczos method applied to the matrix exp(tA*) exp(tA) and exploit the sparseness of A through matrix-vector products. In any of these methods the function Gamma(t) is computed at points of a given coarse grid to localize its maxima, and then maximized by a standard maximization procedure or via an alternating maximization procedure. Results of such computations with some test matrices are reported and analyzed. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free