Quadratic Interpolation and Rayleigh-Ritz Methods for Bifurcation Coefficients

Details Quadratic Interpolation and Rayleigh-Ritz Methods for Bifurcation Coefficients Quadratic Interpolation and Rayleigh-Ritz Methods for Bifurcation Coefficients

2009-03-04

arxiv.org/abs/0903.0686v1

Mathematics

Spectral Theory

34 pages, 4 figures, 1 table

Scientific paper

In this article we study the estimation of bifurcation coefficients in nonlinear branching problems by means of Rayleigh-Ritz approximation to the eigenvectors of the corresponding linearized problem. It is essential that the approximations converge in a norm of sufficient strength to render the nonlinearities continuous. Quadratic interpolation between Hilbert spaces is used to seek sharp rate of convergence results for bifurcation coefficients. Examples from ordinary and partial differential problems are presented.

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