Papers by Junior Peña Delgado
2003 International Conference on Geometric Modeling and Graphics, 2003. Proceedings, 2003
Proceedings Sixth International Conference on Information Visualisation, 2002
In this paper we study the monotonicity preservation of Wang-Ball system and of another system of... more In this paper we study the monotonicity preservation of Wang-Ball system and of another system of polynomials useful in computer-aided geometric design. We also prove that rational Wang-Ball representations are not always monotonicity preserving.
Linear Algebra and its Applications, 2010
Journal of Mathematical Chemistry, 2010
Solving linear systems is often required in chemical problems. Besides, birth and death processes... more Solving linear systems is often required in chemical problems. Besides, birth and death processes occur in many chemical phenomena and the matrices associated to these processes are totally positive, that is, all their minors are nonnegative. Neville elimination is an elimination procedure very useful when dealing with these matrices. Convergence and stability of iterative refinement using Neville elimination are analyzed, in particular when the coefficient matrix is totally positive. Other applications to chemistry are commented and numerical experiments are shown.
Journal of Computational and Applied Mathematics, 2011
Journal of Computational and Applied Mathematics, 2010
Journal of Computational and Applied Mathematics, 2008
Backward stability of the Casteljau algorithm and two more efficient algorithms for polynomial te... more Backward stability of the Casteljau algorithm and two more efficient algorithms for polynomial tensor product surfaces with interest in CAGD is shown. The conditioning of the corresponding bases are compared. These algorithms are also compared with the corresponding Horner algorithm and their higher accuracy is shown. A running error analysis of the algorithms is also carried out providing algorithms which calculate "a posteriori" sharp error bounds simultaneously to the evaluation of the surface without increasing significantly the computational cost.
International Journal of Computer Mathematics, 2009
Computer Aided Geometric Design, 2007
We present examples which show that rational Bézier surfaces are not axially monotonicity preserv... more We present examples which show that rational Bézier surfaces are not axially monotonicity preserving and that surfaces generated by the tensor product of rational bases are not monotonicity preserving. Besides, we prove that surfaces generated by rational functions through Bernstein basis on a triangle are not axially monotonicity preserving.
Computer Aided Geometric Design, 2005
If we can evaluate a curve by means of a corner cutting algorithm, we call the corresponding syst... more If we can evaluate a curve by means of a corner cutting algorithm, we call the corresponding system of functions a corner cutting system. We prove that corner cutting systems are always monotonicity preserving. We obtain weak sufficient conditions for corner cutting systems. Optimal stability properties and properties concerning the supports of the basis functions of corner cutting systems are also analyzed.
Computer Aided Geometric Design, 2003
We consider a blending basis for which we obtain an algorithm for the evaluation of polynomial cu... more We consider a blending basis for which we obtain an algorithm for the evaluation of polynomial curves with linear time complexity and we prove that it is a normalized totally positive basis. Therefore, it simultaneously satisfies efficiency and shape preservation. We also provide the corner cutting algorithm for obtaining the Bézier polygon from the control polygon with respect this basis. Related bases with additional properties are also considered.
Computer Aided Geometric Design, 2007
All normalized totally positive bases satisfy the progressive iterative approximation property. T... more All normalized totally positive bases satisfy the progressive iterative approximation property. The normalized B-basis has optimal shape preserving properties and we prove that it satisfies the progressive iterative approximation property with the fastest convergence rates. A similar result for tensor product surfaces is also derived.
Computer Aided Geometric Design, 2011
This note revisits the progressive iteration approximation property and some recent modifications... more This note revisits the progressive iteration approximation property and some recent modifications from the point of view of iterative methods for solving linear systems. In particular we show the connection with the classical Richardson iteration and modified Richardson iteration. We propose to use GMRES as an alternative iterative method. Numerical experiments achieve much better approximations with only few iterations, which can be explained by an interpretation of the GMRES method.
Computer-Aided Design, 2012
Two recent tools for constructing interpolating curves and surfaces are the progressive iteration... more Two recent tools for constructing interpolating curves and surfaces are the progressive iteration approximation (PIA) and the geometric algorithm. This communication has two main goals. On the one hand, we show that the proof of Theorem 1 of [5] on the convergence of the geometric algorithm is not correct. On the other hand, we clarify the difference between several variants of the PIA iterations by introducing the idea of preconditioned PIA iterations.
BIT Numerical Mathematics, 2013
Applied Mathematics Letters, 2009
Applied Mathematics and Computation, 2013
es un dispositivo con capacidad de cortar la corriente eléctrica de un receptor o instalación con... more es un dispositivo con capacidad de cortar la corriente eléctrica de un receptor o instalación con la posibilidad de ser accionado a distancia, que tiene dos posiciones de funcionamiento: una estable o de reposo, cuando no recibe acción alguna por parte del circuito de mando, y otra inestable, cuando actúa dicha acción. Este tipo de funcionamiento se llama de "todo o nada".
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Papers by Junior Peña Delgado