MATEMATIC - Ponencias, comunicaciones, etc.
http://hdl.handle.net/10017/24317
MATEMATIC - Ponencias, comunicaciones, etc.Thu, 06 Oct 2022 00:17:30 GMT2022-10-06T00:17:30ZFitness landscape analysis in the optimization of coefficients of curve parametrizations
http://hdl.handle.net/10017/45090
Fitness landscape analysis in the optimization of coefficients of curve parametrizations
Sendra Pons, Juan Rafael; Winkler, Stephan M.
Parametric representations of geometric objects, such as curves or surfaces, may have unnecessarily huge integer coefficients. Our goal is to search for an alternative parametric representation of the same object with significantly smaller integer coefficients. We have developed and implemented an evolutionary algorithm that is able to find solutions to this problem in an efficient as well as robust way. In this paper we analyze the fitness landscapes associated with this evolutionary algorithm. We here discuss the use of three different strategies that are used to evaluate and order partial solutions. These orderings lead to different landscapes of combinations of partial solutions in which the optimal solutions are searched. We see that the choice of this ordering strategy has a huge inuence on the characteristics of the resulting landscapes, which are in this paper analyzed using a set of metrics, and also on the quality of the solutions that can be found by the subsequent evolutionary search.
Este documento se considera que es una ponencia de congresos en lugar de un capítulo de libro.; Computer Aided Systems Theory - EUROCAST 2017, 19-24 February, Las Palmas de Gran Canaria, Spain.; J.R. Sendra is member of the Research Group ASYNACS (Ref.CT-CE2019/683)
Fri, 26 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10017/450902018-01-26T00:00:00ZOn Symbolic Solutions of Algebraic Partial Differential Equations
http://hdl.handle.net/10017/20704
On Symbolic Solutions of Algebraic Partial Differential Equations
Grasegger, Georg; Sendra Pons, Juan Rafael; Lastra Sedano, Alberto; Winkler , Franz
In this paper we present a general procedure for solving rst-order autonomous
algebraic partial di erential equations in two independent variables.
The method uses proper rational parametrizations of algebraic surfaces
and generalizes a similar procedure for rst-order autonomous ordinary
di erential equations. We will demonstrate in examples that, depending on
certain steps in the procedure, rational, radical or even non-algebraic solutions
can be found. Solutions computed by the procedure will depend on
two arbitrary independent constants.
The final version of this paper appears in Grasegger G., Lastra A., Sendra J.R. and
Winkler F. (2014). On symbolic solutions of algebraic partial differential equations, Proc.
CASC 2014 SpringerVerlag LNCS 8660 pp. 111-120. DOI 10.1007/978-3-319-10515-4_9
and it is available at at Springer via http://DOI 10.1007/978-3-319-10515-4_9
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10017/207042014-01-01T00:00:00ZCovering of surfaces parametrized without projective base points
http://hdl.handle.net/10017/20682
Covering of surfaces parametrized without projective base points
Sendra Pons, Juan Rafael; Sevilla, David; Villarino Cabellos, Carlos
We prove that every a ne rational surface, parametrized by means of an a ne rational parametrization without projective base points, can be covered by at most three parametrizations.
Moreover, we give explicit formulas for computing the coverings. We provide two di erent approaches: either
covering the surface with a surface parametrization plus a curve parametrization plus a point, or with the original parametrization plus two surface reparametrizations of it.
This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in "Sendra J.R., Sevilla D., Villarino C. Covering of surfaces parametrized without projective base points. Proc. ISSAC2014 ACM Press, pages 375-380, 2014,
ISBN:978-1-4503-2501-1". http://dx.doi.org/10.1145/2608628.2608635
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10017/206822014-01-01T00:00:00ZOn the approximate parametrization problem of algebraic curves
http://hdl.handle.net/10017/20520
On the approximate parametrization problem of algebraic curves
Rueda Pérez, Sonia Luisa; Sendra Pons, Juana; Sendra Pons, Juan Rafael
The problem of parametrizing approximately algebraic curves and surfaces is an active
research field, with many implications in practical applications. The problem can be treated
locally or globally. We formally state the problem, in its global version for the case of algebraic
curves (planar or spatial), and we report on some algorithms approaching it, as well as on the
associated error distance analysis.
Proceedings of Applications of Computer Algebra : ACA 2013. Málaga
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10017/205202013-01-01T00:00:00Z