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1.
András Kroó 《Constructive Approximation》1989,5(1):405-414
According to the Hobby-Rice theorem for anyn-dimensional subspaceU
n
ofL
1([a, b], ) ( positive, finite, nonatomic) there exist points =s
0x
1x
m+1=b, where 0mn, such that
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2.
We show that the size of the 1-norm condition number of the univariate Bernstein basis for polynomials of degree n is O (2n
/ √n). This is consistent with known estimates [3], [5] for p = 2 and p = ∞ and leads to asymptotically correct results for the p-norm condition number of the Bernstein basis for any p with 1 ≤ p ≤ ∞. 相似文献
3.
Jeffrey S. Geronimo Evans M. Harrell II Walter Van Assche 《Constructive Approximation》1988,4(1):403-417
We consider the abstract measures, known as thedensity- of- states measures, associated with the asymptotic distribution of eigenvalues of infinite banded Hermitian matrices. Two widely used definitions of these measures are shown to be equivalent, even in the unbounded case, and we prove that the density of states is invariant under certain, possibly unbounded, perturbations. Also considered are measures associated with the asymptotic distribution of eigenvalues of rescaled unbounded matrices. These measures are associated with the so-called contracted spectrum when the matrices are tridiagonal. Finally, we produce several examples clarifying the nature of the density of states.Communicated by Paul Nevai. 相似文献
4.
A. J. Duran 《Constructive Approximation》1997,13(2):271-286
A technique to find the asymptotic behavior of the ratio between a polynomialss
n and thenth orthonormal polynomial with respect to a positive measureμ is shown. Using it, some new results are found and a very simple proof for other classics is given. 相似文献
5.
In the table of multivariate rational interpolants the entries are arranged such that the row index indicates the number of numerator coefficients and the column index the number of denominator coefficients. If the homogeneous system of linear equations defining the denominator coefficients has maximal rank, then the rational interpolant can be represented as a quotient of determinants. If this system has a rank deficiency, then we identify the rational interpolant with another element from the table using less interpolation conditions for its computation and we describe the effect this dependence of interpolation conditions has on the structure of the table of multivariate rational interpolants. In the univariate case the table of solutions to the rational interpolation problem is composed of triangles of so-called minimal solutions, having minimal degree in numerator and denominator and using a minimal number of interpolation conditions to determine the solution.Communicated by Dietrich Braess. 相似文献
6.
M. Taghavi 《Rendiconti del Circolo Matematico di Palermo》1999,48(2):237-242
The quotient of
divided by
, whereP is a self-inversive and unimodular polynomial of any degree, dominates an absolute constantK>1. A 1989 paper gaveK=1.0252 on which its authors conjetured that the best constant is
. We supply counter examples to their claim and provide a partial result for whenever theL
q norm is replaced by some “discrete” type norm.
Research supported by the Shiraz University Grant 72-SC-784-432. 相似文献
7.
Motivated by the problem of multivariate scattered data interpolation, much interest has centered on interpolation by functions of the form
|