Results 271 to 280 of about 61,972 (313)
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On Generating Discrete Orthogonal Bivariate Polynomials
BIT Numerical Mathematics, 2002This paper is concerned with an algorithm for recursively generating discrete orthogonal bivariate polynomials on a finite set \(S\left \{ (x_j,y_j) \right \} _{j=1}^n \in \mathbb R ^2 \) with respect to a weight vector \(m=(m_1,\dots ,m_n)\) having unit mass.
Huhtanen, Marko, Larsen, Rasmus Munk
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Discrete orthogonal polynomials – polynomial modification of a classical functional
Journal of Difference Equations and Applications, 2001Polynomial modifications of a classical discrete linear functional are examined in detail, in particular when the new linear functional remains classical. New addition formulas are deduced for Charlier, Meixner and Hahn polynomials from the Christoffei representation and results are also given for a particular generalized Meixner family.
Ronveaux, André, Salto, L.
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Discrete classical orthogonal polynomials
Journal of Difference Equations and Applications, 1998We find necessary and sufficient conditions for the difference equation of hypergeometric type to have polynomial solutions , which are orthogonal, that is Traditionallydμ(x) is a positive measure but here we allow it to be a signed measure. We then show that the usual restrictions on parameters in discrete classical orthogonal polynomials can be ...
Kwon, KH Kwon, Kil Hyun +3 more
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MeixnerNet: Adaptive and Robust Spectral Graph Neural Networks with Discrete Orthogonal Polynomials
arXiv.orgSpectral Graph Neural Networks (GNNs) have achieved state-of-the-art results by defining graph convolutions in the spectral domain. A common approach, popularized by ChebyNet, is to use polynomial filters based on continuous orthogonal polynomials (e.g.,
Hüseyin Göksu
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Discrete Invariant Curve Flows, Orthogonal Polynomials, and Moving Frame
, 2020In this paper, an orthogonal polynomials-based (OPs-based) approach to generate discrete moving frames and invariants is developed. It is shown that OPs can provide explicit expressions for the discrete moving frame as well as the associated difference
Bao Wang +3 more
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Discrete orthogonal polynomials on an infinite lattice
, 2013P. Bleher, Karl Liechty
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Difference Equations and Discriminants for Discrete Orthogonal Polynomials
The Ramanujan Journal, 2005Let \(\{p_n(x)\}\) be a sequence of discrete orthogonal polynomials satisfy orthogonality relation \[ \sum_{l=s}^t p_m(l)p_n(l)w(l)=\kappa_m \delta_{m,n} \qquad \qquad \sum_{l=s}^t w(l)=1 \] where \(w\) is a weight function. \(l \in \{s, s+1, \dots, t\} \subset \mathbf{R}\), \(s\) is finite but \(t\) is finite or infinite.
Ismail, Mourad E. H. +2 more
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Discrete orthogonal matrix polynomials
Analysis Mathematica, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Orthogonal Polynomials and a Discrete Boundary Value Problem II
SIAM Journal on Mathematical Analysis, 1992The present paper is a continuation of an earlier work (see the paper reviewed above). The monotonicity condition of the sequence \(\{\beta_ n\}\) is given up. The result is applied to the measures \(d\mu(x)=(1-x^ 2)^ \alpha| x|^{2\beta+1}dx\) and \(d\mu(x)=| x|^{2\alpha+1} e^{-x^ 2}dx\), \(\alpha,\beta>-1\).
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Level Statistics of Discrete Schrödinger Equations and Orthogonal Polynomials
Journal of the Physical Society of Japan, 1993Summary: One-dimensional discrete Schrödinger equations (tight binding models) are analyzed from the viewpoint of level statistics. The energy levels of them are identical to the zeroes of the corresponding orthogonal polynomials. The level densities and local level correlations are calculated in the cases related to classical orthogonal polynomials ...
Nagao, Taro, Wadati, Miki
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