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31.
Michel Grabisch Christophe Labreuche 《Journal of Mathematical Analysis and Applications》2008,343(2):1080-1097
The Choquet integral w.r.t. a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of n[0,1]. We take this basic fact as a starting point to define the Choquet integral in a very general way, using the geometric realization of lattices and their natural triangulation, as in the work of Koshevoy.A second aim of the paper is to define a general mechanism for the bipolarization of ordered structures. Bisets (or signed sets), as well as bisubmodular functions, bicapacities, bicooperative games, as well as the Choquet integral defined for them can be seen as particular instances of this scheme.Lastly, an application to multicriteria aggregation with multiple reference levels illustrates all the results presented in the paper. 相似文献
32.
Antonia M. Delgado Jeffrey S. Geronimo Plamen Iliev Yuan Xu 《Constructive Approximation》2009,30(1):71-91
The one-variable Bernstein–Szegő theory for orthogonal polynomials on the real line is extended to a class of two-variable
measures. The polynomials orthonormal in the total degree ordering and the lexicographical ordering are constructed and their
recurrence coefficients discussed.
相似文献
33.
Vito Vitrih 《Annali dell'Universita di Ferrara》2008,54(2):349-359
In this paper, four-pencil lattices on tetrahedral partitions are studied. The explicit representation of a lattice, based
upon barycentric coordinates, enables us to extend the lattice from a single tetrahedron to a tetrahedral partition. It is
shown that the number of degrees of freedom is equal to the number of vertices of the tetrahedral partition. The proof is
based on a lattice split approach.
相似文献
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Ternary subdivision schemes compare favorably with their binary analogues because they are able to generate limit functions with the same (or higher) smoothness but smaller support.In this work we consider the two issues of local tension control and conics reproduction in univariate interpolating ternary refinements. We show that both these features can be included in a unique interpolating 4-point subdivision method by means of non-stationary insertion rules that do not affect the improved smoothness and locality of ternary schemes. This is realized by exploiting local shape parameters associated with the initial polyline edges. 相似文献
37.
38.
In this paper, a family of interpolation neural network operators are introduced. Here, ramp functions as well as sigmoidal functions generated by central B-splines are considered as activation functions. The interpolation properties of these operators are proved, together with a uniform approximation theorem with order, for continuous functions defined on bounded intervals. The relations with the theory of neural networks and with the theory of the generalized sampling operators are discussed. 相似文献
39.
We improve upon the method of Zhu and Zhu [A method for directly finding the denominator values of rational interpolants, J. Comput. Appl. Math. 148 (2002) 341–348] for finding the denominator values of rational interpolants, reducing considerably the number of arithmetical operations required for their computation. In a second stage, we determine the points (if existent) which can be discarded from the rational interpolation problem. Furthermore, when the interpolant has a linear denominator, we obtain a formula for the barycentric weights which is simpler than the one found by Berrut and Mittelmann [Matrices for the direct determination of the barycentric weights of rational interpolation, J. Comput. Appl. Math. 78 (1997) 355–370]. Subsequently, we give a necessary and sufficient condition for the rational interpolant to have a pole. 相似文献
40.
Shuo Tang Yan Liang 《高等学校计算数学学报(英文版)》2007,16(3):271-288
Both the expansive Newton's interpolating polynomial and the Thiele-Werner's interpolation are used to construct a kind of bivariate blending Thiele-Werner's osculatory rational interpolation. A recursive algorithm and its characteristic properties are given. An error estimation is obtained and a numerical example is illustrated. 相似文献