Displaying similar documents to “Laguerre-like methods with corrections for the inclusion of polynomial zeros.”

On nodal sets and nodal domains on S 2 and 2

Alexandre Eremenko, Dmitry Jakobson, Nikolai Nadirashvili (2007)

Annales de l’institut Fourier

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We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on S 2 . We also construct a solution of the equation Δ u = u in 2 that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.

The effect of rounding errors on a certain class of iterative methods

Ioannis Argyros (2000)

Applicationes Mathematicae

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In this study we are concerned with the problem of approximating a solution of a nonlinear equation in Banach space using Newton-like methods. Due to rounding errors the sequence of iterates generated on a computer differs from the sequence produced in theory. Using Lipschitz-type hypotheses on the mth Fréchet derivative (m ≥ 2 an integer) instead of the first one, we provide sufficient convergence conditions for the inexact Newton-like method that is actually generated on the computer....