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Manuel López Galván

Publications and source records attributed to Manuel López Galván.

4 recordsLinked to original sources
arXiv2017

The multivariate bisection algorithm

The aim of this paper is the study of the bisection method in $\mathbb{R}^n$. In this work we propose a multivariate bisection method supported by the Poincaré-Miranda theorem in order to solve non-linear system of equations. Given an initial cube verifying the hypothesis of Poincaré-Miranda theorem the algorithm performs congruent refinements throughout its center by generating a root approximation. Throughout preconditioning we will prove the local convergence of this new root finder methodology and moreover we will perform a numerical implementation for the two dimensional case.

math.NA↗
arXiv2015

Riemannian metrics in infinite dimensional self-adjoint operator groups

The aim of this paper is the study of the geodesic distance in operator groups with several Riemannian metrics. More precisely we study the geodesic distance in self-adjoint operator groups with the left invariant Riemannian metric induced by the infinite trace and extend known results about the completeness of some classical Banach-Lie groups to this general class.

math.DG↗
arXiv2015

Riemannian metrics on an infinite dimensional symplectic group

The aim of this paper is the geometric study of the symplectic operators which are a perturbation of the identity by a Hilbert-Schmidt operator. This subgroup of the symplectic group was introduced in Pierre de la Harpe's classical book of Banach-Lie groups. Throughout this paper we will endow the tangent spaces with different Riemannian metrics. We will use the minimal curves of the unitary group and the positive invertible operators to compare the length of the geodesic curves in each case. Moreover we will study the completeness of the symplectic group with the geodesic distance.

math.DG↗