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Toric embedded resolutions of quasi-ordinary hypersurface singularities

Pedro D. González Pérez — 2003

Annales de l’institut Fourier

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...

A unifying convergence analysis of Newton's method for twice Fréchet-differentiable operators

I. K. Argyros; D. González — 2015

Applicationes Mathematicae

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.

Una demostración constructiva de un homeomorfismo entre P y SO(3).

J. M. Almira; P. D. González — 2001

Gaceta de la Real Sociedad Matemática Española

Local convergence of a one parameter fourth-order Jarratt-type method in Banach spaces

I. K. Argyros; D. González; S. K. Khattri — 2016

Commentationes Mathematicae Universitatis Carolinae

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 $R$ -order four with reduced computational cost, BIT Numer. Math. 49 (2009), 325–342] cannot be used to solve equations...

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