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991.
Ming-Jun Lai 《Numerical Algorithms》1992,2(1):33-38
We describe an algorithm to compute the B-nets of bivariate box splines on a three-or four-directional mesh. Two pseudo Fortran programs for those B-nets are given.Research supported by a Faculty Grant From the University of Utah Research Committee. 相似文献
992.
A second look at the authors' [BDR1], [BDR2] characterization of the approximation order of a Finitely generated Shift-Invariant
subspace S(Φ) of L
2
(R
d
) results in a more explicit formulation entirely in terms of the (Fourier transform of the) generators of the subspace. Further, when the generators satisfy a certain technical condition, then, under the mild assumption that
the set of 1-periodizations of the generators is linearly independent, such a space is shown to provide approximation order
k if and only if contains a ψ (necessarily unique) satisfying . The technical condition is satisfied, e.g., when the generators are at infinity for some ρ>k+d . In the case of compactly supported generators, this recovers an earlier result of Jia [J1], [J2].
March 19. 1996. Date revised: September 6, 1996. 相似文献
993.
Supported by the National Science Foundation of China 相似文献
994.
995.
Jun Furuya 《Monatshefte für Mathematik》2002,137(2):129-156
Let χ be a Dirichlet character modulo k > 1, and F
χ(n) the arithmetical function which is generated by the product of the Riemann zeta-function and the Dirichlet L-function corresponding to χ in . In this paper we study the asymptotic behaviour of the exponential sums involving the arithmetical function F
χ(n). In particular, we study summation formulas for these exponential sums and mean square formulas for the error term.
Received April 17, 2001; in revised form April 2, 2002 相似文献
996.
Multistep interpolation of scattered data by compactly supported radial basis functions requires hierarchical subsets of the
data. This paper analyzes thinning algorithms for generating evenly distributed subsets of scattered data in a given domain
in ℝ
d
. 相似文献
997.
J. M. Carnicer 《Numerical Algorithms》1991,1(2):155-176
For givenk-convex data, ak-convex interpolant is sought, so that a certain convex functional related with thek-th derivative is minimized.Partially supported by C.I.C.Y.T. PS87/0060. 相似文献
998.
Summary A method for the construction of a set of data of interpolation in several variables is given. The resulting data, which are either function values or directional derivatives values, give rise to a space of polynomials, in such a way that unisolvence is guaranteed. The interpolating polynomial is calculated using a procedure which generalizes the Newton divided differences formula for a single variable. 相似文献
999.
Annie Cuyt 《BIT Numerical Mathematics》1986,26(1):71-79
Several definitions of multivariate Padé approximants have been introduced during the last decade. We will here consider all types of definitions based on the choice that the coefficients in numerator and denominator of the multivariate Padé approximant are defined by means of a linear system of equations. In this case a determinant representation for the multivariate Padé approximant exists. We will show that a general recursive algorithm can be formulated to compute a multivariate Padé approximant given by any definition of this type. Here intermediate results in the recursive computation scheme will also be multivariate Padé approximants. Up to now such a recursive computation of multivariate Padé approximants only seemed possible in some special cases. 相似文献
1000.
We show that ifw(x)=exp(–|x|), then in the case =1 for every continuousf that vanishes outside the support of the corresponding extremal measure there are polynomialsP
n of degree at mostn such thatw
n
P
n uniformly tends tof, and this is not true when <1. these=" are=" the=" missing=" cases=" concerning=" approximation=" by=" weighted=" polynomials=" of=" the=">1.>w
n
P
n wherew is a Freud weight. Our second theorem shows that even if we are only interested in approximation off on the extremal support, the functionf must still vanish at the endpoints, and we actually determine the (sequence of) largest possible intervals where approximation is possible. We also briefly discuss approximation by weighted polynomials of the formW(anx)P
n
(x).Communicated by Edward B. Saff. 相似文献