Bifurcations via singular value decompositions

摘要

We study the relation between bifurcation theory and singular value decomposition in numerical analysis. Given a nonlinear equation, we give a local analysis in a neighborhood of a solution via the Liapunov-Schmidt method and the singular value decomposition. The theorem is applicable to regular, turning, or bifurcation points. A numerical method for global bifurcation problems based on the above analysis is presented.