Sufficient conditions for the convergence of the Magnus expansion

2007/11/15 by Fernando Casas · 4 citations
Computer Science · Engineering · Mathematics · #Matrix Theory and Algorithms #Numerical methods for differential equations #Stability and Controllability of Differential Equations #math.CA #msc:34A12 #msc:34A30

paper · pdf · doi:10.1088/1751-8113/40/50/006

published as J. Phys. A: Math. Theor. 40 (2007), 15001-15017 · 20 pages

arxiv created 2007/11/15 · openalex publication_date 2007/11/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Two different sufficient conditions are given for the convergence of the Magnus expansion arising in the study of the linear differential equation Y ′ = A ( t ) Y . The first one provides a bound on the convergence domain based on the norm of the operator A ( t ). The second condition links the convergence of the expansion with the structure of the spectrum of Y ( t ), thus yielding a more precise characterization. Several examples are proposed to illustrate the main issues involved and the information on the convergence domain provided by both conditions.

Citations

• On the exponential solution of differential equations for a linear operator

Cited by

• The Magnus expansion and some of its applications
• Long-time electron spin storage via dynamical suppression of hyperfine-induced decoherence in a quantum dot
• Rigorous bounds on the performance of a hybrid dynamical-decoupling quantum-computing scheme
• Distance bounds on quantum dynamics