共查询到20条相似文献,搜索用时 734 毫秒
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Henri Cohen. 《Mathematics of Computation》1996,65(216):1681-1699
We show how the usual algorithms valid over Euclidean domains, such as the Hermite Normal Form, the modular Hermite Normal Form and the Smith Normal Form can be extended to Dedekind rings. In a sequel to this paper, we will explain the use of these algorithms for computing in relative extensions of number fields.
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ON HERMITE MATRIX POLYNOMIALS AND HERMITE MATRIX FUNCTIONS 总被引:1,自引:0,他引:1
In this paper properties of Hermite matrix polynomials and Hermite matrix functions are studied. The concept ot total set with respect to a matrix functional is introduced and the total property of the Hermite matrix polynomials is proved. Asymptotic behaviour of Hermite matrix polynomials is studied and the relationship of Hermite matrix functions with certain matrix differential equations is developed. A new expression of the matrix exponential for a wide class of matrices in terms of Hermite matrix polynomials is proposed. 相似文献
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Vector and Hermite subdivision schemes both act on vector data, but since the latter one interprets the vectors as function
values and consecutive derivatives they differ by the “renormalization” of the Hermite scheme in any step. In this paper we
give an algebraic factorization method in one and several variables to relate any Hermite subdivision scheme that satisfies
the so–called spectral condition to a vector subdivision scheme. These factorizations are natural extensions of the “zero
at π” condition known for the masks of refinable functions. Moreover, we show how this factorization can be used to investigate
different forms of convergence of the Hermite scheme and why the multivariate situation is conceptionally more intricate than
the univariate one. Finally, we give some examples of such factorizations. 相似文献
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The Hermite rank appears in limit theorems involving long memory. We show that a Hermite rank higher than one is unstable when the data is slightly perturbed by transformations such as shift and scaling. We carry out a “near higher order rank analysis” to illustrate how the limit theorems are affected by a shift perturbation that is decreasing in size. We also consider the case where the deterministic shift is replaced by centering with respect to the sample mean. The paper is a companion of Bai and Taqqu (2017) which discusses the instability of the Hermite rank in the statistical context. 相似文献
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Ming Zhang 《Applied Numerical Mathematics》2011,61(5):666-674
The purpose of this paper is to put forward a kind of Hermite interpolation scheme on the unit sphere. We prove the superposition interpolation process for Hermite interpolation on the sphere and give some examples of interpolation schemes. The numerical examples shows that this method for Hermite interpolation on the sphere is feasible. And this paper can be regarded as an extension and a development of Lagrange interpolation on the sphere since it includes Lagrange interpolation as a particular case. 相似文献
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In many practical problems, it is often desirable to interpolate not only the function values but also the values of derivatives up to certain order, as in the Hermite interpolation. The Hermite interpolation method by radial basis functions is used widely for solving scattered Hermite data approximation problems. However, sometimes it makes more sense to approximate the solution by a least squares fit. This is particularly true when the data are contaminated with noise. In this paper, a weighted meshless method is presented to solve least squares problems with noise. The weighted meshless method by Gaussian radial basis functions is proposed to fit scattered Hermite data with noise in certain local regions of the problem’s domain. Existence and uniqueness of the solution is proved. This approach has one parameter which can adjust the accuracy according to the size of the noise. Another advantage of the weighted meshless method is that it can be used for problems in high dimensions with nonregular domains. The numerical experiments show that our weighted meshless method has better performance than the traditional least squares method in the case of noisy Hermite data. 相似文献
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《Journal of Computational and Applied Mathematics》2012,236(4):565-574
In a recent paper, we investigated factorization properties of Hermite subdivision schemes by means of the so-called Taylor factorization. This decomposition is based on a spectral condition which is satisfied for example by all interpolatory Hermite schemes. Nevertheless, there exist examples of Hermite schemes, especially some based on cardinal splines, which fail the spectral condition. For these schemes (and others) we provide the concept of a generalized Taylor factorization and show how it can be used to obtain convergence criteria for the Hermite scheme by means of factorization and contractivity. 相似文献
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Jean-Louis Merrien 《Journal of Computational and Applied Mathematics》2011,236(4):565-574
In a recent paper, we investigated factorization properties of Hermite subdivision schemes by means of the so-called Taylor factorization. This decomposition is based on a spectral condition which is satisfied for example by all interpolatory Hermite schemes. Nevertheless, there exist examples of Hermite schemes, especially some based on cardinal splines, which fail the spectral condition. For these schemes (and others) we provide the concept of a generalized Taylor factorization and show how it can be used to obtain convergence criteria for the Hermite scheme by means of factorization and contractivity. 相似文献
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Kuznetsov Alexey Kwaśnicki Mateusz 《Journal of Fourier Analysis and Applications》2019,25(3):1053-1079
There exist many ways to build an orthonormal basis of \(\mathbb {R}^N\), consisting of the eigenvectors of the discrete Fourier transform (DFT). In this paper we show that there is only one such orthonormal eigenbasis of the DFT that is optimal in the sense of an appropriate uncertainty principle. Moreover, we show that these optimal eigenvectors of the DFT are direct analogues of the Hermite functions, that they also satisfy a three-term recurrence relation and that they converge to Hermite functions as N increases to infinity.
相似文献12.
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Jianing Sun 《Journal of Fourier Analysis and Applications》2009,15(5):739-752
In this paper, we construct a new family of Hermite-type interpolating scaling vectors with compact support, of which the
Hermite interpolation property generalizes the existing results of interpolating scaling vectors and Hermite interpolants.
In terms of the Hermite interpolatory mask, we characterize the Hermite interpolation property, approximation property and
symmetry property in detail. To illustrate these results, several examples with compact support and high smoothness are exhibited
at the end of this paper. 相似文献
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Budh Nashier 《Monatshefte für Mathematik》1987,104(2):119-124
LetR be a commutative Noetherian ring with identity. The Hermite dimension ofR is defined to be the least integerr such that every stably freeR-module of rank greater thanr is free. In this paper we study ringsR obtained upon inversion of elements of a given ringA. We show that the Hermite dimension ofR does not depend on the Hermite dimension ofA, it depends on the Krull dimension ofA. 相似文献
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Energy minimization has been widely used for constructing curve and surface in the fields such as computer-aided geometric design, computer graphics. However, our testing examples show that energy minimization does not optimize the shape of the curve sometimes. This paper studies the relationship between minimizing strain energy and curve shapes, the study is carried out by constructing a cubic Hermite curve with satisfactory shape. The cubic Hermite curve interpolates the positions and tangent vectors of two given endpoints. Computer simulation technique has become one of the methods of scientific discovery, the study process is carried out by numerical computation and computer simulation technique. Our result shows that: (1) cubic Hermite curves cannot be constructed by solely minimizing the strain energy; (2) by adoption of a local minimum value of the strain energy, the shapes of cubic Hermite curves could be determined for about 60 percent of all cases, some of which have unsatisfactory shapes, however. Based on strain energy model and analysis, a new model is presented for constructing cubic Hermite curves with satisfactory shapes, which is a modification of strain energy model. The new model uses an explicit formula to compute the magnitudes of the two tangent vectors, and has the properties: (1) it is easy to compute; (2) it makes the cubic Hermite curves have satisfactory shapes while holding the good property of minimizing strain energy for some cases in curve construction. The comparison of the new model with the minimum strain energy model is included. 相似文献
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In this paper we study a class of multivariate Hermite interpolation problem on 2~d nodes with dimension d ≥ 2 which can be seen as a generalization of two classical Hermite interpolation problems of d = 2. Two combinatorial identities are firstly given and then the regularity of the proposed interpolation problem is proved. 相似文献
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Xingping Sun 《Numerical Algorithms》1994,7(2):253-268
In this paper, we study cardinal Hermite interpolation by using positive definite functions. Among other things, we establish a procedure that employs the multiquadrics for cardinal Hermite interpolation. 相似文献
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The main results of this paper offer sufficient conditions in order that an approximate lower Hermite–Hadamard type inequality implies an approximate convexity property. The failure of such an implication with constant error term shows that functional error terms should be considered for the inequalities and convexity properties in question. The key for the proof of the main result is a Korovkin type theorem which enables us to deduce the approximate convexity property from the approximate lower Hermite–Hadamard type inequality via an iteration process. 相似文献
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Cem Kaano?lu 《Journal of Computational and Applied Mathematics》2011,235(16):4878-4887
The purpose of this paper is to introduce and discuss a more general class of multiple Hermite polynomials. In this work, the explicit forms, operational formulas and a recurrence relation are obtained. Furthermore, we derive several families of bilinear, bilateral and mixed multilateral finite series relationships and generating functions for the generalized multiple Hermite polynomials. 相似文献
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A matrix A ∈ Mn(C) is called generalized normal provided that there is a positive definite Hermite matrix H such that HAH is normal. In this paper, these matrices are investigated and their canonical form, invariants and relative properties in the sense of congruence are obtained. 相似文献