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81.
An embedding criterion for interpolation spaces is formulated and applied to the study of the Riesz basis property in the L
2,g space of eigenfunctions of an indefinite Sturm–Liouville problem u=gu on the interval (-1,1) with the Dirichlet boundary conditions, provided that the function g(x) changes sign at the origin. In particular, the basis property criterion is established for an odd g(x). Some connections with stability in interpolation scales are discussed. 相似文献
82.
In this paper we present a new limit relation for the equidistant Lagrange interpolation polynomials to |x|, (0, 1] on the internal [–1, 1]. The result extends a well-known result of D. L. Berman and S. M. Losinskii. Furthermore, we briefly discuss on a possible connection of the limit relation to another prominent constant in best uniform polynomial approximation for |x| - the so-called Bernstein constant. 相似文献
83.
In this paper, we study orthogonal polynomials with respect to the bilinear form (f, g)
S
= V(f) A
V(g)
T
+ <u, f
(N)
g
(N)V(f) =(f(c
0), f "(c
0), ..., f
(n – 1)
0(c
0), ..., f(c
p
), f "(c
p
), ..., f
(n – 1)
p(c
p
))
u is a regular linear functional on the linear space P of real polynomials, c
0, c
1, ..., c
p
are distinct real numbers, n
0, n
1, ..., n
p
are positive integer numbers, N=n
0+n
1+...+n
p
, and A is a N × N real matrix with all its principal submatrices nonsingular. We establish relations with the theory of interpolation and approximation. 相似文献
84.
Zernike多项式是光机热集成分析中实现光、机、热各分析软件之间数据传递的重要工具。许多光学元件表面形状并不满足Zernike多项式的正交性条件,使有限元分析不能精确拟合光学元件表面变形及变形产生的各项像差。讨论影响Zernike正交性的几个因素,详细介绍将有限元分析得到的光学表面变形数据导入光学分析软件的一种新方法——干涉图插值法。该方法避开Zernike多项式拟合,在去除镜面刚体位移后将镜面畸变精确地表示成干涉图数据,直接生成数据接口。 相似文献
85.
When the stagnation temperature of a perfect gas increases, the specific heats and their ratio do not remain constant any
more and start to vary with this temperature. The gas remains perfect and its state equation always remains valid, except
it will be called a calorically imperfect gas. The aim of this research is to develop the relations of the necessary thermodynamics
and geometrical ratios and to study the supersonic flow at high temperature (lower than the threshold of dissociation). The
results are found by the resolution of nonlinear algebraic equations and integration of complex analytical functions where
the exact calculation is impossible. The dichotomy method is used to solve the nonlinear equation, and the Simpson algorithm
is used for the numerical integration of the found integrals. A condensation of the nodes is used, since the functions to
be integrated have a high gradient at the extremity of the interval of integration. A comparison is made with a calorifcally
perfect gas to determine the error of this. An application is made for air in a supersonic nozzle.
The text was submitted by the authors in English. 相似文献
86.
SUN Jin-Feng HU Qiu-Bo ZHU Zun-Lue WANG Xiao-Fei ZHANG Ji-Cai 《理论物理通讯》2007,47(6):1121-1124
Elastic scattering properties of the ultracold interaction for the triplet state of ^133Cs and ^85Rb atoms are studied using two kinds of potentials by the same phase Ф. One is the interpolation potential, and another is Lennard-Jones potential (LJl2,6 ). The radial Schrodtinger equation is also solved using two computational methods, the semiclassical method (WKB), and the Numerov method. Our results are found to be in an excellent agreement with the more recent theoretical values. It shows that the two potentials and methods are applicable for studying ultracold collisions between the mixing alkali atoms. 相似文献
87.
本文给出了基于Lascenov多项式零点(0,2)-插值正则性的充要条件,并给出基多项式存在时的明显表达式。 相似文献
88.
Winfried Sickel Frauke Sprengel 《Journal of Computational Analysis and Applications》1999,1(3):263-288
We investigate the order of convergence of periodic interpolation on sparse grids (blending interpolation) in the framework of tensor products of Nikol'skij–Besov spaces. To this end, we make use of the uniformity of the considered tensor norms and provide a unified approach to error estimates for the interpolation of univariate periodic functions from Nikol'skij–Besov spaces. 相似文献
89.
Gregory E. Fasshauer 《Advances in Computational Mathematics》1999,10(1):81-96
We show how conditionally negative definite functions on spheres coupled with strictly completely monotone functions (or functions
whose derivative is strictly completely monotone) can be used for Hermite interpolation. The classes of functions thus obtained
have the advantage over the strictly positive definite functions studied in [17] that closed form representations (as opposed
to series expansions) are readily available. Furthermore, our functions include the historically significant spherical multiquadrics.
Numerical results are also presented.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
90.
Fornberg Bengt; Flyer Natasha; Hovde Susan; Piret Cecile 《IMA Journal of Numerical Analysis》2008,28(1):121-142