共查询到20条相似文献,搜索用时 15 毫秒
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We show how to construct stable quasi-interpolation schemes in the bivariate spline spaces S
d
r
(Δ) with d⩾ 3r + 2 which achieve optimal approximation order. In addition to treating the usual max norm, we also give results in the L
p norms, and show that the methods also approximate derivatives to optimal order. We pay special attention to the approximation
constants, and show that they depend only on the smallest angle in the underlying triangulation and the nature of the boundary
of the domain.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
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V. Paulauskas 《Lithuanian Mathematical Journal》2009,49(4):426-445
In the paper, we approximate the distribution function of a sum of independent nonidentically distributed bivariate random
vectors by the distribution function of a stable vector and estimate the accuracy of such an approximation. The obtained general
result is only a little bit worse when compared with known estimates for the case of multivariate independent and identically
distributed random vectors or univariate nonidentically distributed summands. We also apply the result obtained to a specific
scheme arising when considering the so-called Increment-Ratio Statistics. 相似文献
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In this work we will consider He's variational iteration method for solving second-order initial value problems. We will discuss the use of this approach for solving several important partial differential equations. This method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. This procedure is a powerful tool for solving the large amount of problems. Using the variational iteration method, it is possible to find the exact solution or an approximate solution of the problem. This technique provides a sequence of functions which converges to the exact solution of the problem. Our emphasis will be on the convergence of the variational iteration method. In the current paper this scheme will be investigated in details and efficiency of the approach will be shown by applying the procedure on several interesting and important models. 相似文献
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We develop methods for constructing sets of points which admit Lagrange and Hermite type interpolation by spaces of bivariate splines on rectangular and triangular partitions which are uniform, in general. These sets are generated by building up a net of lines and by placing points on these lines which satisfy interlacing properties for univariate spline spaces. 相似文献
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In this paper, quasi-interpolating splines are used to approximate the Cauchy principal value integral $$J(w_{\alpha \beta } f;\lambda ): = \smallint - _{ - 1}^1 w_{\alpha \beta } (x)\frac{{f(x)}}{{x - \lambda }}dx, \lambda \in ( - 1,1)$$ where $w_{\alpha \beta } (x): = (1 - x)^\alpha (1 + x)^\beta ,\alpha ,\beta > - 1.$ . We prove uniform convergence for the quadrature rules proposed here and give an algorithm for the numerical evaluation of these rules. 相似文献
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In this paper we present an approximation problem of parametric curves and surfaces from a Lagrange or Hermite data set. In particular, we study an interpolation problem by minimizing some functional on a Sobolev space that produces the new notion of interpolating variational spline. We carefully establish a convergence result. Some specific cases illustrate the generality of this work. 相似文献
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Some choices of denominators are given which ensure the geometrical convergence of certain convergence of bivariate two-point Padé-type approximants to functions being holomorphic on certain domains 相似文献
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Gao Junbin 《分析论及其应用》1991,7(2):41-50
We study the determining set for bivariate spline spacesS
k
o
on type-1 triangulation of square using B-net techniques. We further construct the interpolation schemes for these spline
spaces that are unisolvent for any function f of Cσ. 相似文献
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The approximation of solutions to partial differential equations by tensorial separated representations is one of the most efficient numerical treatment of high dimensional problems. The key step of such methods is the computation of an optimal low-rank tensor to enrich the obtained iterative tensorial approximation. In variational problems, this step can be carried out by alternating minimization (AM) technics, but the convergence of such methods presents a real challenge. In the present work, the convergence of rank-one AM algorithms for a class of variational linear elliptic equations is studied. More precisely, we show that rank-one AM-sequences are in general bounded in the ambient Hilbert tensor space and are compact if a uniform non-orthogonality condition between iterates and the reaction term is fulfilled. In particular, if a rank-one AM-sequence is weakly convergent then it converges strongly and the common limit is a solution of the rank-one optimization problem. 相似文献
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I. V. Konnov 《Computational Mathematics and Mathematical Physics》2006,46(4):541-547
For variational inequalities in a finite-dimensional space, the convergence of a regularization method is examined in the case of a nonmonotone basic mapping. It is shown that a fairly general sufficient condition for the existence of solutions to the original problem also guarantees the convergence and existence of solutions to perturbed problems. Examples of applications to problems on order intervals are presented. 相似文献
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Gabriele H. Greco Maria Pia Moschen Eliane Quelho Frota Rezende 《Annali dell'Universita di Ferrara》1998,44(1):27-39
Kaleva [9] has studied the relationships between the metric convergencesH andD of fuzzy convex sets on Euclidean spaces. The distanceH between two fuzzy set is given by Hausdorff distance of their sendographs, whileD is the supremum of the Hausdorff distances of the level sets corresponding to the fuzzy sets. The aim of this paper is to
compareH andD with the variational convergence, called γ-convergence (see De Giorgi and Franzoni [3]). Our analysis which is carried out
in the setting of metric spaces (not necessarily locally compact or vector spaces), improves Kaleva's results.
Sunto Kaleva ha investigato in [9] le relazioni esistenti tra due convergenze metriche, detteH eD, di sottoinsiemi fuzzy di spazi euclidei finito-dimensionali. In questo articolo le convergenzeH eD (la loro definizione dipende dalla distanza di Hausdorff tra insiemi compatti) sono confrontate con la convergenza variazionale, detta γ-convergenza, introdotta da De Giorgi and Franzoni in [3] nel contesto degli spazi topologici. Tale confronto con la γ-convergenza (vedi Teorema 3.7), svolto nell'ambito degli spazi metrici (non necessariamente, localmente compatti o lineari) migliora ed estende i precedenti risultati di Kaleva.相似文献
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We explore convergence notions for bivariate functions that yield convergence and stability results for their maxinf (or minsup) points. This lays the foundations for the study of the stability of solutions to variational inequalities, the solutions of inclusions, of Nash equilibrium points of non-cooperative games and Walras economic equilibrium points, of fixed points, of solutions to inclusions, the primal and dual solutions of convex optimization problems and of zero-sum games. These applications will be dealt with in a couple of accompanying papers. 相似文献
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This paper introduces an Ishikawa type iterative algorithm for finding approximating solutions of a class of multi-valued
variational inclusion problems. Characterization of strong convergence of this iterative method is established.
L. C. Ceng’s research partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher
Education Institutions of MOE, China and the Dawn Program Foundation in Shanghai.
S. Schaible’s research partially supported by the National Science Council of Taiwan.
This research was partially supported by the grant NSC 96-2628-E-110-014-MY3. 相似文献
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In this paper we give some results about convergence of non
coercive quadratic integral functionals by examining the behaviour of coefficients.
We apply our results to semicontinuity problems and we illustrate
them by some examples.AMS Subject Classification: 40A10, 49J45. 相似文献