共查询到20条相似文献,搜索用时 15 毫秒
1.
A local bivariate C1 quasi-interpolating spline operator with a four directional mesh is considered and studied. Based on the above operator we
present cubature formulas for 2-D singular integrals, defined in the Hadamard finite part sense. Convergence results are obtained
for a wide class of functions. Moreover numerical tests are given.
Sponsored by M.U.R.S.T. and C.N.R. of Italy. 相似文献
2.
《Journal of Computational and Applied Mathematics》2005,173(1):21-37
We investigate spline quasi-interpolants defined by C1 bivariate quadratic B-splines on nonuniform type-2 triangulations and by discrete linear functionals based on a fixed number of triangular mesh-points either in the support or close to the support of such B-splines.We show they can approximate a real function and its partial derivatives up to an optimal order and we derive local and global upper bounds.We also present some numerical and graphical results. 相似文献
3.
In this paper cubature formulas based on bivariate C
1 local polynomial splines with a four directional mesh [4] are generated and studied. Some numerical results with comparison
with other methods are given. Moreover the method proposed is applied to the numerical evaluation of 2‐D singular integrals
defined in the Hadamard finite part sense. Computational features, convergence properties and error bounds are proved.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
4.
5.
设p_1,p_2,p_3为不同的奇素数,c1是整数.给出了Pell方程组x~2-(c~2-1)y~2=y~2-2p_1p_2p_3z~2=1的所有非负整数解(x,y,z),从而推广了Keskin (2017)和Cipu(2018)等人的结果. 相似文献
6.
Amat Sergio Levin David Ruiz-Álvarez Juan Trillo Juan C. Yáñez Dionisio F. 《Numerical Algorithms》2022,91(1):51-79
Numerical Algorithms - In many applications, it is useful to use piecewise polynomials that satisfy certain regularity conditions at the joint points. Cubic spline functions emerge as good... 相似文献
7.
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
8.
The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H
1 (ℝ
n
× ℝ
m
) to the Lebesgue space L
1(ℝ
n
× ℝ
m
) and their commutators with Lipschitz functions from the Hardy space H
1 (ℝ
n
× ℝ
m
) to the Lebesgue space L
q
(ℝ
n
× ℝ
m
) for some q > 1. 相似文献
9.
10.
11.
12.
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
13.
14.
M. G. Cimoroni 《分析论及其应用》1997,13(4):1-12
In this paper the author presents a method for the numerical solution of a 2-D Cauchy principal value of the form
where S is a domain with a continuous boundary. By using polar coordinates, the integral is reduced to the form
where
the finite-part of the integral. We construct the relative product rule based on quasi-inter polating splines.
Convergence results are proved and numerical examples are given. 相似文献
15.
16.
17.
18.
It is shown that bivariate interpolatory splines defined on a rectangleR can be characterized as being unique solutions to certain variational problems. This variational property is used to prove the uniform convergence of bivariate polynomial splines interpolating moderately smooth functions at data which includes interpolation to values on a rectangular grid. These results are then extended to bivariate splines defined on anL-shaped region.This research was supported by a University of Kansas General Research Grant. 相似文献
19.
Bo Einarsson 《BIT Numerical Mathematics》1968,8(4):279-286
The most used formula for calculation of Fourier integrals is Filon's formula which is based on approximation of the function by a quadratic in each double interval. In order to obtain a better approximation we use the cubic spline fit. The method is not restricted to equidistant points, but the final formulas are only derived in this case. Test computations show that the spline formula may be superior to Filon's formula. 相似文献
20.