On solving an isospectral flow

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:308

Article

Kaur, Amandeep¹ 

[1] Univ Cambridge, Ctr Math Sci, Dept Appl Math & Theoret Phys, Wilberforce Rd, Cambridge CB3 0WA, England

关键词: Isospectral flow;    Eigenvalues;    Magnus expansion;    Lie algebra;    Binary trees;   

DOI  :  10.1016/j.cam.2016.05.033

来源: Elsevier

【 摘 要 】

In this paper we expand the solution of the matrix ordinary differential system, originally due to Bloch and Iserles, of the form X' = [N, X-2], t >= 0, X(0) = X-0 is an element of Sym(n), N is an element of so(n), where Sym(n) denotes the space of real n x n symmetric matrices and so(n) denotes the Lie algebra of real n x n skew-symmetric matrices. The flow is solved using explicit Magnus expansion, which respects the isospectrality of the system. We represent the terms of expansion as binary rooted trees and deduce an explicit formalism to construct the trees recursively. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free