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1.
Hermite interpolation with trigonometric polynomials 总被引:10,自引:0,他引:10
Franz-Jürgen Delvos 《BIT Numerical Mathematics》1993,33(1):113-123
Interpolation methods of Hermite type in translation invariant spaces of trigonometric polynomials for any position of interpolation points and any number of derivatives are constructed. For the case of an odd number of interpolation conditions-periodic trigonometric polynomials of minimum order are chosen as interpolation functions while for the case of an even number of interpolation conditions-antiperiodic trigonometric polynomials of minimum order are appropriate. 相似文献
2.
The rank-k-numerical range of an n×n matrix A is defined as
3.
Emily Sergel 《Advances in Applied Mathematics》2012,48(1):99-105
We define and study biorthogonal sequences of polynomials over noncommutative rings, generalizing previous treatments of biorthogonal polynomials over commutative rings and of orthogonal polynomials over noncommutative rings. We extend known recurrence relations for specific cases of biorthogonal polynomials and prove a general version of Favard?s theorem. 相似文献
4.
Summary We find necessary and sufficient conditions for the regularity (or unique solvability) of a trigonometric interpolation problem on three equidistant nodes in [0, 2) where the data are almost Hermitian. We shall show that in many cases the conditions only depend upon the number of even and odd derivatives prescribed in the problem. In general such a simplification seems to be difficult.Dedicated to the memory of Alexander M. Ostrowski on occasion of the 100th anniversary of his birth 相似文献
5.
By establishing a cosine analogue of a result of Askey and Steinig on a monotonic sine sum, this paper sharpens and unifies several results associated with Young's inequality for the partial sums of k
–1 cosk. 相似文献
6.
In this contribution we analyze rational spectral transformations related to associated polynomials with respect to probability measures supported on the interval [−1, 1]. The connection with rational spectral transformations of measures supported on the unit circle using the Szeg? transformation is presented. 相似文献
7.
Toufik Mansour 《Discrete Mathematics》2006,306(12):1161-1176
We study generating functions for the number of even (odd) permutations on n letters avoiding 132 and an arbitrary permutation τ on k letters, or containing τ exactly once. In several interesting cases the generating function depends only on k and is expressed via Chebyshev polynomials of the second kind. 相似文献
8.
In this paper we analyze a perturbation of a nontrivial positive measure supported on the unit circle. This perturbation is the inverse of the Christoffel transformation and is called the Geronimus transformation. We study the corresponding sequences of monic orthogonal polynomials as well as the connection between the associated Hessenberg matrices. Finally, we show an example of this kind of transformation. 相似文献
9.
M. Bayat 《Linear algebra and its applications》2011,435(11):2936-2941
In this paper, we give a generalization of a determinantal identity posed by Charles R. Johnson about minors of a Toeplitz matrix satisfying a specific matrix identity. These minors are those appear in the Dodgson’s condensation formula. 相似文献
10.
Eric S. Egge 《Discrete Mathematics》2007,307(14):1792-1800
Several authors have examined connections between restricted permutations and Chebyshev polynomials of the second kind. In this paper we prove analogues of these results for colored permutations. First we define a distinguished set of length two and length three patterns, which contains only 312 when just one color is used. Then we give a recursive procedure for computing the generating function for the colored permutations which avoid this distinguished set and any set of additional patterns, which we use to find a new set of signed permutations counted by the Catalan numbers and a new set of signed permutations counted by the large Schröder numbers. We go on to use this result to compute the generating functions for colored permutations which avoid our distinguished set and any layered permutation with three or fewer layers. We express these generating functions in terms of Chebyshev polynomials of the second kind and we show that they are special cases of generating functions for involutions which avoid 3412 and a layered permutation. 相似文献
11.
Anita Buckley 《Linear algebra and its applications》2010,433(4):758-780
Let C be a smooth curve in P2 given by an equation F=0 of degree d. In this paper we consider elementary transformations of linear pfaffian representations of C. Elementary transformations can be interpreted as actions on a rank 2 vector bundle on C with canonical determinant and no sections, which corresponds to the cokernel of a pfaffian representation. Every two pfaffian representations of C can be bridged by a finite sequence of elementary transformations. Pfaffian representations and elementary transformations are constructed explicitly. For a smooth quartic, applications to Aronhold bundles and theta characteristics are given. 相似文献
12.
Using two different elementary approaches we derive a global and a local perturbation theorem on polynomial zeros that significantly
improve the results of Ostrowski (Acta Math 72:99–257, 1940), Elsner et al. (Linear Algebra Appl 142:195–209, 1990). A comparison
of different perturbation bounds shows that our results are better in many cases than the similar local result of Beauzamy
(Can Math Bull 42(1):3–12, 1999). Using the matrix theoretical approach we also improve the backward stability result of Edelman
and Murakami (Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, SIAM, Philapdelphia, 1994; Math Comput 64:210–763,
1995). 相似文献
13.
John R. Stembridge 《Annals of Combinatorics》1998,2(4):365-385
We describe a characteristic-free algorithm for reducing an algebraic variety defined by the vanishing of a set of integer polynomials. In very special cases, the algorithm can be used to decide whether the number of points on a variety, as the ground field varies over finite fields, is a polynomial function of the size of the field. The algorithm is then used to investigate a conjecture of Kontsevich regarding the number of points on a variety associated with the set of spanning trees of any graph. We also prove several theorems describing properties of a (hypothetical) minimal counterexample to the conjecture, and produce counterexamples to some related conjectures.Partially supported by NSF Grant DMS-9700787 and RIMS, Kyoto University. 相似文献
14.
Ronan Quarez 《Linear algebra and its applications》2012,436(9):3642-3660
We give an elementary proof, only using linear algebra, of a result due to Helton, Mccullough and Vinnikov, which says that any polynomial over the reals can be written as the determinant of a symmetric affine linear pencil. We give explicit determinantal representation formulas and extend our results to polynomials with coefficients in a ring of characteristic different from 2. 相似文献
15.
We consider the problem of approximating a Boolean functionf∶{0,1} n →{0,1} by the sign of an integer polynomialp of degreek. For us, a polynomialp(x) predicts the value off(x) if, wheneverp(x)≥0,f(x)=1, and wheneverp(x)<0,f(x)=0. A low-degree polynomialp is a good approximator forf if it predictsf at almost all points. Given a positive integerk, and a Boolean functionf, we ask, “how good is the best degreek approximation tof?” We introduce a new lower bound technique which applies to any Boolean function. We show that the lower bound technique yields tight bounds in the casef is parity. Minsky and Papert [10] proved that a perceptron cannot compute parity; our bounds indicate exactly how well a perceptron canapproximate it. As a consequence, we are able to give the first correct proof that, for a random oracleA, PP A is properly contained in PSPACE A . We are also able to prove the old AC0 exponential-size lower bounds in a new way. This allows us to prove the new result that an AC0 circuit with one majority gate cannot approximate parity. Our proof depends only on basic properties of integer polynomials. 相似文献
16.
This paper considers the problem of showing that every pair of binary trees with the same number of leaves parses a common word under a certain simple grammar. We enumerate the common parse words for several infinite families of tree pairs and discuss several ways to reduce the problem of finding a parse word for a pair of trees to that for a smaller pair. The statement that every pair of trees has a common parse word is equivalent to the statement that every planar graph is four-colorable, so the results are a step toward a language theoretic proof of the four color theorem. 相似文献
17.
Morris Newman 《Linear and Multilinear Algebra》2013,61(4):363-366
Let Rbe a principal ideal ringRn the ring of n× nmatrices over R, and dk (A) the kth determinantal divisor of Afor 1 ? k? n, where Ais any element of Rn , It is shown that if A,BεRn , det(A) det(B:) ≠ 0, then dk (AB) ≡ 0 mod dk (A) dk (B). If in addition (det(A), det(B)) = 1, then it is also shown that dk (AB) = dk (A) dk (B). This provides a new proof of the multiplicativity of the Smith normal form for matrices with relatively prime determinants. 相似文献
18.
We consider some Nikol'skij-type inequalities, thus inequalities between different metrics of a function, for almost periodic
trigonometric polynomials. Some basic methods of probability theory are applied to prove the existence of the distribution
function for an almost periodic function in the sense of Besicovitch. Finally, the Maximal function of Hardy and Littlewood
is considered and maximal inequalities on Besicovitch spaces are proved.
Received: 23 July 1998 / Revised version: 8 March 1999 相似文献
19.
We study the connection between orthogonal polynomials in several variables and families of commuting symmetric operators of a special form. 相似文献
20.
We present a new method to study 4-dimensional linear spaces of skew-symmetric matrices of constant co-rank 2, based on rank 2 vector bundles on P3 and derived category tools. The method allows one to prove the existence of new examples of size 10×10 and 14×14 via instanton bundles of charge 2 and 4 respectively, and it provides an explanation for what used to be the only known example (Westwick 1996 [25]). We also give an algorithm to construct explicitly a matrix of size 14 of this type. 相似文献