DMA - Artículoshttps://hdl.handle.net/10481/313622023-03-30T01:18:58Z2023-03-30T01:18:58ZQuadratic Decomposition of Bivariate Orthogonal PolynomialsBranquinho, AmílcarPérez Fernández, Teresa Encarnaciónhttps://hdl.handle.net/10481/809162023-03-29T06:58:51ZQuadratic Decomposition of Bivariate Orthogonal Polynomials
Branquinho, Amílcar; Pérez Fernández, Teresa Encarnación
We describe the relation between the systems of bivariate
orthogonal polynomial associated to a symmetric weight function and
associated to some particular Christoffel modifications of the quadratic
decomposition of the original weight. We analyze the construction of a
symmetric bivariate orthogonal polynomial sequence from a given one,
orthogonal to a weight function defined on the first quadrant of the
plane. In this description, a sort of B¨acklund type matrix transformations
for the involved three term matrix coefficients plays an important
role. Finally, we take as a case study relations between the classical
orthogonal polynomials defined on the ball and those on the simplex.
Approximation of 3D trapezoidal fuzzy data using radial basis functionsGonzález Rodelas, PedroPasadas Fernández, Miguelhttps://hdl.handle.net/10481/806192023-03-16T08:52:03ZApproximation of 3D trapezoidal fuzzy data using radial basis functions
González Rodelas, Pedro; Pasadas Fernández, Miguel
We present a new methodology to approximate a trapezoidal fuzzy numbers set by using smoothing radial basis functions (RBFs). The methodology uses different error and similarity indices to determine and compare the accuracy of the approximation of the given trapezoidal fuzzy data. For the proposed approximation method a fuzzy radial basis functions type are defined, called fuzzy smoothing radial basis functions under tension. The computation of one of these approximation functions from a given trape-zoidal fuzzy data set is described and some convergence results are proved. Finally, some examples in two-dimensions are given to compare the behavior of the presented method by using the proposed error and similarity indices for different configurations of the fuzzy smoothing radial basis functions under tension.
Harris-type results on geometric and subgeometric convergence to equilibrium for stochastic semigroupsCañizo Rincón, José AlfredoMischler, Stéphanehttps://hdl.handle.net/10481/800752023-02-20T10:55:29ZHarris-type results on geometric and subgeometric convergence to equilibrium for stochastic semigroups
Cañizo Rincón, José Alfredo; Mischler, Stéphane
We provide simple and constructive proofs of Harris-type the-orems on the existence and uniqueness of an equilibrium and the speed of equilibration of discrete-time and continuous-time stochastic semigroups. Our results apply both to cases where the relaxation speed is exponential (also called geomet-ric) and to those with no spectral gap, with non-exponential speeds (also called subgeometric). We give constructive esti-mates in the subgeometric case and discrete-time statements which seem both to be new. The method of proof also differs from previous works, based on semigroup and interpolation arguments, valid for both geometric and subgeometric cases with essentially the same ideas. In particular, we present very simple new proofs of the geometric case.
Filling holes under non-linear constraintsCustódio, Ana LuisaFortes Escalona, Miguel ÁngelSajo-Castelli, A. M.https://hdl.handle.net/10481/800582023-02-20T07:40:29ZFilling holes under non-linear constraints
Custódio, Ana Luisa; Fortes Escalona, Miguel Ángel; Sajo-Castelli, A. M.
In this paper we handle the problem of filling the hole in the graphic of a surface by means of a patch that joins the original surface with C1-smoothness and fulfills an additional non-linear geometrical constraint regarding its area or its mean curvature at some points. Furthermore, we develop a technique to estimate the optimum area that the filling patch is expected to have that will allow us to determine optimum filling patches by means of a system of linear and quadratic equations. We present several numerical and graphical examples showing the effectiveness of the proposed method.
C-1-Cubic Quasi-Interpolation Splines over a CT Refinement of a Type-1 TriangulationBenharzallah, HaithemBarrera Rosillo, Domingohttps://hdl.handle.net/10481/797832023-02-09T09:57:02ZC-1-Cubic Quasi-Interpolation Splines over a CT Refinement of a Type-1 Triangulation
Benharzallah, Haithem; Barrera Rosillo, Domingo
C1 continuous quasi-interpolating splines are constructed over Clough–Tocher refinement
of a type-1 triangulation. Their Bernstein–Bézier coefficients are directly defined from the known
values of the function to be approximated, so that a set of appropriate basis functions is not required.
The resulting quasi-interpolation operators reproduce cubic polynomials. Some numerical tests are
given in order to show the performance of the approximation scheme.