We build two embedded resolution procedures of a quasi-ordinary singularity of complex
analytic hypersurface, by using toric morphisms which depend only on the characteristic
monomials associated to a quasi-ordinary projection of the singularity. This result
answers an open problem of Lipman in Equisingularity and simultaneous resolution of
singularities, Resolution of Singularities, Progress in Mathematics No. 181, 2000, 485-
503. In the first procedure the singularity is...
We provide a local as well as a semilocal convergence analysis for Newton's method using unifying hypotheses on twice Fréchet-differentiable operators in a Banach space setting. Our approach extends the applicability of Newton's method. Numerical examples are also provided.
We present a local convergence analysis of a one parameter Jarratt-type method. We use this method to approximate a solution of an equation in a Banach space setting. The semilocal convergence of this method was recently carried out in earlier studies under stronger hypotheses. Numerical examples are given where earlier results such as in [Ezquerro J.A., Hernández M.A., New iterations of -order four with reduced computational cost, BIT Numer. Math. 49 (2009), 325–342] cannot be used to solve equations...
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