共查询到20条相似文献,搜索用时 10 毫秒
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L. A. Sakhnovich 《Functional Analysis and Its Applications》2004,38(1):72-74
We study extremal nonnegative polynomials in several variables. Our approach makes substantial use of block Toeplitz matrices. Note that the blocks of these matrices are themselves Toeplitz matrices. 相似文献
3.
V. V. Khlobystov 《Journal of Mathematical Sciences》2001,104(6):1677-1681
By using earlier results, we find solutions of two extremal problems on sets of interpolation polynomials for functions of several variables. 相似文献
4.
We study asymptotics for orthogonal polynomials and other extremalpolynomials on infinite discrete sets, typical examples beingthe Meixner polynomials and the Charlier polynomials. Followingideas of Rakhmanov, Dragnev and Saff, weshow that the asymptoticbehaviour is governed by a constrained extremal energy problemfor logarithmic potentials, which can be solved explicitly.We give formulas for the contracted zero distributions, thenth root asymptotics and the asymptotics of the largest zeros.1991 Mathematics Subject Classification: 42C05, 33C25, 31A15. 相似文献
5.
V. N. Dubinin 《Mathematical Notes》2005,78(5-6):768-772
For polynomials P(z) with real coefficients having a fixed leading coefficient and satisfying the conditions P(z) ∈ [?1, 1] for z ∈ [?1, 1] and P(z) ∈ [?1, 1] if P′(z) = 0, we obtain new covering theorems, a Bernshtein-type inequality, and inequalities for the coefficients. The proofs are based on the use of univalent conformal mappings. 相似文献
6.
Franz Peherstorfer 《Journal of Approximation Theory》2001,111(2):738
In this paper we show that for a given set of l real disjoint intervals El=lj=1 [a2j−1, a2j] and given >0 there exists a real polynomial
and a set of l disjoint intervals El=lj=1 [ã2j−1, ã2j] with ElEl and (ã1, …, ã2l)−(a1, …, a2l)max<, such that
−1([−1, 1])=El. The statement follows by showing how to get in a constructive way by a continuous deformation procedure from a minimal polynomial on El with respect to the maximum norm a polynomial mapping of El. 相似文献
7.
IfPis a continuousm-homogeneous polynomial on a real normed space andPis the associated symmetricm-linear form, the ratio P/P always lies between 1 andmm/m!. We show that, as in the complex case investigated by Sarantopoulos (1987,Proc. Amer. Math. Soc.99, 340–346), there areP's for which P/P=mm/m! and for whichPachieves norm if and only if the normed space contains an isometric copy of ℓm1. However, unlike the complex case, we find a plentiful supply of such polynomials providedm4. 相似文献
8.
Mathematical Notes - 相似文献
9.
Jeffrey J. Holt 《Journal of Approximation Theory》1997,88(3):275-303
In this paper we present two classes of extremal approximating functions. These functions have the property that they are entire, have finite exponential type, and provide excellent approximations along the real line for a specific set of functions. One class of functions provides majorants and minorants, while the other class minimizes theL1-norm on the real line. As applications we construct extremal trigonometric polynomials and obtain an inequality involving almost periodic trigonometric polynomials. 相似文献
10.
Let p
n
be the n th orthonormal polynomial with respect to a positive finite measure μ supported by Δ=[-1,1] . It is well known that, uniformly on compact subsets of C/Δ , and, for a large class of measures μ , where g
Ω
(z) is Green's function of with pole at infinity. It is also well known that these limit relations give convergence of the diagonal Padé approximants
of the Markov function to f on Ω with a certain geometric speed measured by g
Ω
(z) .
We prove corresponding results when we restrict the freedom of p
n
by preassigning some of the zeros. This means that the Padé approximants are replaced by Padé-type approximants where some
of the poles are preassigned. We also replace Δ by general compact subsets of C.
July 12, 1995. Date revised: October 1, 1996. 相似文献
11.
Shi Y. G. 《Journal of Approximation Theory》1993,73(3)
In this paper some characterizations of the regularity of (0, 2) interpolation are given. 相似文献
12.
S. P. Sidorov 《Journal of Approximation Theory》2002,118(2):188-201
In this paper, we will show that Lagrange interpolatory polynomials are optimal for solving some approximation theory problems concerning the finding of linear widths.In particular, we will show that
, where
n is a set of the linear operators with finite rank n+1 defined on
−1,1], and where
n+1 denotes the set of polynomials p=∑i=0n+1aixi of degreen+1 such that an+11. The infimum is achieved for Lagrange interpolatory polynomial for nodes
. 相似文献
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13.
Petar Petrov 《Monatshefte für Mathematik》2006,151(1):165-171
In this work we investigate polynomials of maximal (minimal) arc-length in the interval [−1, 1] amongst all monic polynomials
of fixed degree n with n real zeros in [−1, 1]. 相似文献
14.
Petar Petrov 《Monatshefte für Mathematik》2006,147(2):165-171
In this work we investigate polynomials of maximal (minimal) arc-length in the interval [−1, 1] amongst all monic polynomials
of fixed degree n with n real zeros in [−1, 1]. 相似文献
15.
D. Kleinbock 《Geometric And Functional Analysis》2003,13(2):437-466
It was proved in the paper [KM1] that the properties of almost all
points of being not very well (multiplicatively) approximable are
inherited by nondegenerate in (read: not contained in a proper
affine subspace) smooth submanifolds. In this paper we consider submanifolds
which are contained in proper a.ne subspaces, and prove
that the aforementioned Diophantine properties pass from a subspace
to its nondegenerate submanifold. The proofs are based on a correspondence
between multidimensional Diophantine approximation and
dynamics of lattices in Euclidean spaces.
Submitted: March 2002; Revision: August 2002 相似文献
16.
V. V. Khlobystov 《Journal of Mathematical Sciences》2001,104(6):1672-1676
We give solutions of two extremal problems, a generalization of a result of W. Porter on an interpolation polynomial in L2(a,b) with minimal norm, which we get here in an abstract Hilbert space with a measure, and an analogue of a theorem of M. Golomb and H. Weinberger for a bounded set of operator interpolants. 相似文献
17.
A. B. J. Kuijlaars 《Constructive Approximation》2000,16(4):559-589
We consider the asymptotic zero behavior of polynomials that are extremal with respect to slowly decaying weights on [0, ∈fty) , such as the log-normal weight \exp(-γ
2
log
2
x) . The zeros are contracted by taking the appropriate d
n
th roots with d
n
→∈fty . The limiting distribution of the contracted zeros is described in terms of the solution of an extremal problem in logarithmic
potential theory with a circular symmetric external field.
November 23, 1998. Date revised: February 8, 1999. Date accepted: March 2, 1999. 相似文献
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Richard J. Fateman 《Studies in Applied Mathematics》1974,53(2):145-155
This paper examines the time for computing integer powers of a class of polynomials in one or several variables. A member f of the class of “sparse” polynomials can be characterized by the number of nonzero terms, t, in the representation of f. Where, for power 4, the most obvious methods result in multiplications, a method is presented which requires fewer than multiplications. This algorithm requires, for t » n » 1 about tn/n! + O(tn ? 1 /(2(n ? 2)!)) multiplications, which is proved to be a lower-bound on the computation. 相似文献
20.
《Journal of Complexity》1999,15(3):299-316
Lower bounds for the error of quadrature formulas with positive weights are proved. We get intractability results for quasi-Monte Carlo methods and, more generally, for positive formulas. We consider general classes of functions but concentrate on lower bounds for relatively small classes of trigonometric polynomials. We also conjecture that similar lower bounds hold for arbitrary quadrature formulas and state different equivalent conjectures concerning positive definiteness of certain matrices and certain extremal problems for trigonometric polynomials. We also study classes of functions with weighted norms where some variables are “more important” than others. Positive quadrature formulas are then tractable iff the sum of the weights is bounded. 相似文献