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Relevant bibliographies by topics / Hermite's Polynomial

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Academic literature on the topic 'Hermite's Polynomial'

Author: Grafiati

Published: 5 June 2025

Last updated: 25 June 2025

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Journal articles on the topic "Hermite's Polynomial"

1

Butt, Saad Ihsan, Khuram Ali Khan, and Josip Pečarić. "Popoviciu type inequalities via Hermite's polynomial." Mathematical Inequalities & Applications, no. 4 (2016): 1309–18. http://dx.doi.org/10.7153/mia-19-96.

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Cheng, Kaimin. "New Permutation Reversed Dickson Polynomials over Finite Fields." Algebra Colloquium 30, no. 01 (2022): 111–20. http://dx.doi.org/10.1142/s1005386723000093.

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Let [Formula: see text] be an odd prime, and [Formula: see text], [Formula: see text] be nonnegative integers. Let [Formula: see text] be the reversed Dickson polynomial of the [Formula: see text]-th kind. In this paper, by using Hermite's criterion, we study the permutational properties of the reversed Dickson polynomials [Formula: see text] over finite fields in the case of [Formula: see text] with [Formula: see text]. In particular, we provide some precise characterizations for [Formula: see text] being permutation polynomials over finite fields with characteristic [Formula: see text] when [Formula: see text], or [Formula: see text], or [Formula: see text].

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Khan, M. Adil, S. Ivelić Bra anović, and Josip Pečarić. "Generalizations of Sherman's inequality by Hermite's interpolating polynomial." Mathematical Inequalities & Applications, no. 4 (2016): 1181–92. http://dx.doi.org/10.7153/mia-19-87.

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4

Heinig, Georg, and Fadhel Al-Musallam. "Hermite's formula for vector polynomial interpolation with applications to structured matrices." Applicable Analysis 70, no. 3-4 (1998): 331–45. http://dx.doi.org/10.1080/00036819808840695.

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WAUBKE, HOLGER. "BOUNDARY ELEMENT METHOD FOR ISOTROPIC MEDIA WITH RANDOM SHEAR MODULI." Journal of Computational Acoustics 13, no. 01 (2005): 229–58. http://dx.doi.org/10.1142/s0218396x05002530.

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Green's functions for elastic solids with random properties are usually derived by means of the perturbation method. This paper deals with a new approach that has the potential to deal with a large variability of random shear modulus based on the transformation of a polynomial chaos. The deterministic Green's functions for stresses and displacements and the principal values in the boundary integrals caused by a pressure load on the surface are nonlinear transformations of the random variables. A series of transformations of the polynomial chaos is used to transform significant parts of the equation. The first operation is a projection of the log normal distributed shear modulus to a series of Hermite's polynomials based on a Gaussian variable. The second operation is the determination of an arbitrary potential of the wave velocity. The last operation, similar to the first one, consists in the determination of an exponential function depending on the inverse of the wave velocity. These operations, together with multiplications and summations, transform the complete relation from the random shear modulus to Green's functions and principal values. The inversion of the system matrix is already derived for the random finite element approach. The operations are independent of the specific problem and can be applied to almost all acoustic media and similar nonlinear problems.

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Kashpur, O. F. "UNDAMENTAL POLYNOMIALS OF HERMITE’SINTERPOLATION FORMULA IN LINEAR NORMAL AND INEUCLIDEAN SPACES." Journal of Numerical and Applied Mathematics, no. 2 (2022): 50–58. http://dx.doi.org/10.17721/2706-9699.2022.2.06.

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In a linear infinite-dimensional space with a scalar product and in a finite-dimensional Euclidean space the interpolation Hermite polynomial with a minimal norm, generated by a Gaussian measure, contains fundamental polynomials are shown. The accuracy of Hermit’s interpolation formulas on polynomials of the appropriate degree are researched.

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Chandra, Bahadur Khadka. "Transformation of Special Relativity into Differential Equation by Means of Power Series Method." International Journal of Basic Sciences and Applied Computing (IJBSAC) 10, no. 1 (2023): 10–15. https://doi.org/10.35940/ijbsac.B1045.0910123.

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Partial differential equations such as those involving Bessel differential function, Hermite’s polynomial, and Legendre polynomial are widely used during the separation of the wave equation in cylindrical and spherical coordinates. Such functions are quite applicable to solve the wide variety of physical problems in mathematical physics and quantum mechanics, but until now, there has been no differential equation capable for handling the problems involved in the realm of special relativity. In order to avert such trouble in physics, this article presents a new kind of differential equation of the form: , where c is the speed of light in a vacuum. In this work, the solution of this equation has been developed via the power series method, which generates a formula that is completely compatible with relativistic phenomena happening in nature. In this highly exciting topic, the particular purpose of this paper is to define entirely a new differential equation to handle physical problems happening in the realm of special relativity.

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Abro, Goh André-Pascal, Kidjégbo Augustin Touré, and Gossrin Jean-Marc Bomisso. "Influence of control parameters on the stabilization of an Euler-Bernoulli flexible beam." Journal of Numerical Analysis and Approximation Theory 53, no. 1 (2024): 109–23. http://dx.doi.org/10.33993/jnaat531-1384.

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In this work, we numerically study the influence of control parameters on the stabilization of a flexible Euler-Bernoulli beam fixed at one end and subjected at the other end to a force control and a punctual moment control proportional respectively to velocity and rotation velocity. First, we analyze the displacement stabilization and the asymptotic behavior of the beam energy using a stable numerical scheme, resulting from the Crank-Nicholson algorithm for time discretization and the finite element method based on the approximation by Hermite's cubic polynomial functions, for discretization in space. Then, by means of the finite element method, we represent the spectrum of the operator associated with this beam problem and we carry out a qualitative study of thelocus of the eigenvalues according to the positive control parameters. From these studies we conclude that rotation velocity control has more effect on the stabilization of the beam compared to velocity control. Finally, this result is confirmed by a sensitivity study on the control parameters involved in the stabilization of the beam.

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Brackx, F., H. De Schepper, N. De Schepper, and F. Sommen. "Hermitean Clifford-Hermite Polynomials." Advances in Applied Clifford Algebras 17, no. 3 (2007): 311–30. http://dx.doi.org/10.1007/s00006-007-0032-0.

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Blel, Mongi. "On some m-symmetric generalized hypergeometric d-orthogonal polynomials." Filomat 38, no. 4 (2024): 1279–89. http://dx.doi.org/10.2298/fil2404279b.

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In [9] I. Lamiri and M. Ouni state some characterization theorems for d-orthogonal polynomials of Hermite, Gould-Hopper and Charlier type polynomials. In [3] Y. Ben Cheikh I. Lamiri and M.Ouni give a characterization theorem for some classes of generalized hypergeometric polynomials containing for example, Gegenbauer polynomials, Gould-Hopper polynomials, Humbert polynomials, a generalization of Laguerre polynomials and a generalization of Charlier polynomials. In this work, we introduce a new class D of generalized hypergeometric m-symmetric polynomial sequence containing the Hermite polynomial sequence and Laguerre polynomial sequence. Then we consider a characterization problem consisting in finding the d-orthogonal polynomial sequences in the class D, m ? d. The solution provides new d-orthogonal polynomial sequences to be classified in d-Askey-scheme and also having a m-symmetry property with m ? d. This class contains the Gould-Hopper polynomial sequence, the class considered by Ben Cheikh-Douak, the class considered in [3]. This class contains new d-orthogonal polynomial sequences not belonging to the classA. We derive also in this work the d-dimensional functional vectors ensuring the d-orthogonality of these polynomials. We also give an explicit expression of the d-dimensional functional vector.

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Dissertations / Theses on the topic "Hermite's Polynomial"

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Khan, Mumtaz Ahmad, Abdul Hakim Khan, and Naeem Ahmad. "A study of modified hermite polynomials." Pontificia Universidad Católica del Perú, 2012. http://repositorio.pucp.edu.pe/index/handle/123456789/96880.

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Perrin, D. A. "The application of Hermite polynomials to turbulent diffusion." Thesis, University of Liverpool, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.383496.

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Ahmad, Khan Mumtaz, Khan Abdul Hakim, and Naeem Ahmad. "A study of modified Hermite polynomials of two variables." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96096.

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The present paper is a study of modied Hermite polynomials of two variables Hn(x; y; a) which for a = e reduces to Hermite polynomials of two variables Hn(x; y) due to M.A. Khan and G.S. Abukhammash.<br>El presente artculo se estudian polinomios modicados de Hermite de dos variables Hn(x; y; a) que para a = e se reducen a los polinomios de Hermite de dos variables Hn(x; y) introducidos por M.A. Khan y G.S.Abukhammash.

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Piotrowski, Andrzej. "Classes of Linear Operators and the Distribution of Zeros of Entire Functions." Thesis, University of Hawaii at Manoa, 2007. http://hdl.handle.net/10125/25932.

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Motivated by the work of Pólya, Schur, and Turán, a complete characterization of multiplier sequences for the Hermite polynomial basis is given. Laguerre's theorem and a remarkable curve theorem due to Pólya are generalized. Sufficient conditions for the location of zeros in certain strips in the complex plane are determined. Results pertaining to multiplier sequences and complex zero decreasing sequences for other polynomial sets are established.<br>viii, 178 leaves, bound ; 29 cm.<br>Thesis (Ph. D.)--University of Hawaii at Manoa, 2007.

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Javed, Mohsin. "Algorithms for trigonometric polynomial and rational approximation." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:23a36d72-0299-4c63-98e8-d0aa088c062e.

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This thesis presents new numerical algorithms for approximating functions by trigonometric polynomials and trigonometric rational functions. We begin by reviewing trigonometric polynomial interpolation and the barycentric formula for trigonometric polynomial interpolation in Chapter 1. Another feature of this chapter is the use of the complex plane, contour integrals and phase portraits for visualising various properties and relationships between periodic functions and their Laurent and trigonometric series. We also derive a periodic analogue of the Hermite integral formula which enables us to analyze interpolation error using contour integrals. We have not been able to find such a formula in the literature. Chapter 2 discusses trigonometric rational interpolation and trigonometric linearized rational least-squares approximations. To our knowledge, this is the first attempt to numerically solve these problems. The contribution of this chapter is presented in the form of a robust algorithm for computing trigonometric rational interpolants of prescribed numerator and denominator degrees at an arbitrary grid of interpolation points. The algorithm can also be used to compute trigonometric linearized rational least-squares and trigonometric polynomial least-squares approximations. Chapter 3 deals with the problem of trigonometric minimax approximation of functions, first in a space of trigonometric polynomials and then in a set of trigonometric rational functions. The contribution of this chapter is presented in the form of an algorithm, which to our knowledge, is the first description of a Remez-like algorithm to numerically compute trigonometric minimax polynomial and rational approximations. Our algorithm also uses trigonometric barycentric interpolation and Chebyshev-eigenvalue based root finding. Chapter 4 discusses the Fourier-Padé (called trigonometric Padé) approximation of a function. We review two existing approaches to the problem, both of which are based on rational approximations of a Laurent series. We present a numerical algorithm with examples and compute various type (m, n) trigonometric Padé approximants.

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Marumo, Kohei. "Expansion methods applied to distributions and risk measurement in financial markets." Thesis, Queensland University of Technology, 2007. https://eprints.qut.edu.au/16506/1/Kohei_Marumo_Thesis.pdf.

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Obtaining the distribution of the profit and loss (PL) of a portfolio is a key problem in market risk measurement. However, existing methods, such as those based on the Normal distribution, and historical simulation methods, which use empirical distribution of risk factors, face difficulties in dealing with at least one of the following three problems: describing the distributional properties of risk factors appropriately (description problem); deriving distributions of risk factors with time horizon longer than one day (time aggregation problem); and deriving the distribution of the PL given the distributional properties of the risk factors (risk aggregation problem). Here, we show that expansion methods can provide reasonable solutions to all three problems. Expansion methods approximate a probability density function by a sum of orthogonal polynomials multiplied by an associated weight function. One of the most important advantages of expansion methods is that they only require moments of the target distribution up to some order to obtain an approximation. Therefore they have the potential to be applied in a wide range of situations, including in attempts to solve the three problems listed above. On the other hand, it is also known that expansions lack robustness: they often exhibit unignorable negative density and their approximation quality can be extremely poor. This limits applications of expansion methods in existing studies. In this thesis, we firstly develop techniques to provide robustness, with which expansion methods result in a practical approximation quality in a wider range of examples than investigated to date. Specifically, we investigate three techniques: standardisation, use of Laguerre expansion and optimisation. Standardisation applies expansion methods to a variable which is transformed so that its first and second moments are the same as those of the weight function. Use of Laguerre expansions applies those expansions to a risk factor so that heavy tails can be captured better. Optimisation considers expansions with coefficients of polynomials optimised so that the difference between the approximation and the target distribution is minimised with respect to mean integrated squared error. We show, by numerical examples using data sets of stock index returns and log differences of implied volatility, and GARCH models, that expansions with our techniques are more robust than conventional expansion methods. As such, marginal distributions of risk factors can be approximated by expansion methods. This solves a part of the description problem: the information on the marginal distributions of risk factors can be summarised by their moments. Then we show that the dependence structure among risk factors can be summarised in terms of their cross-moments. This solves the other part of the description problem. We also use the fact that moments of risk factors can be aggregated using their moments and cross-moments, to show that expansion methods can be applied to both the time and risk aggregation problems. Furthermore, we introduce expansion methods for multivariate distributions, which can also be used to approximate conditional expectations and copula densities by rational functions.

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7

Marumo, Kohei. "Expansion methods applied to distributions and risk measurement in financial markets." Queensland University of Technology, 2007. http://eprints.qut.edu.au/16506/.

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Obtaining the distribution of the profit and loss (PL) of a portfolio is a key problem in market risk measurement. However, existing methods, such as those based on the Normal distribution, and historical simulation methods, which use empirical distribution of risk factors, face difficulties in dealing with at least one of the following three problems: describing the distributional properties of risk factors appropriately (description problem); deriving distributions of risk factors with time horizon longer than one day (time aggregation problem); and deriving the distribution of the PL given the distributional properties of the risk factors (risk aggregation problem). Here, we show that expansion methods can provide reasonable solutions to all three problems. Expansion methods approximate a probability density function by a sum of orthogonal polynomials multiplied by an associated weight function. One of the most important advantages of expansion methods is that they only require moments of the target distribution up to some order to obtain an approximation. Therefore they have the potential to be applied in a wide range of situations, including in attempts to solve the three problems listed above. On the other hand, it is also known that expansions lack robustness: they often exhibit unignorable negative density and their approximation quality can be extremely poor. This limits applications of expansion methods in existing studies. In this thesis, we firstly develop techniques to provide robustness, with which expansion methods result in a practical approximation quality in a wider range of examples than investigated to date. Specifically, we investigate three techniques: standardisation, use of Laguerre expansion and optimisation. Standardisation applies expansion methods to a variable which is transformed so that its first and second moments are the same as those of the weight function. Use of Laguerre expansions applies those expansions to a risk factor so that heavy tails can be captured better. Optimisation considers expansions with coefficients of polynomials optimised so that the difference between the approximation and the target distribution is minimised with respect to mean integrated squared error. We show, by numerical examples using data sets of stock index returns and log differences of implied volatility, and GARCH models, that expansions with our techniques are more robust than conventional expansion methods. As such, marginal distributions of risk factors can be approximated by expansion methods. This solves a part of the description problem: the information on the marginal distributions of risk factors can be summarised by their moments. Then we show that the dependence structure among risk factors can be summarised in terms of their cross-moments. This solves the other part of the description problem. We also use the fact that moments of risk factors can be aggregated using their moments and cross-moments, to show that expansion methods can be applied to both the time and risk aggregation problems. Furthermore, we introduce expansion methods for multivariate distributions, which can also be used to approximate conditional expectations and copula densities by rational functions.

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8

Ahy, Nathaniel. "A Comparison between Approximations of Option Pricing Models and Risk-Neutral Densities using Hermite Polynomials." Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-413732.

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Berglund, Filip. "Asymptotics of beta-Hermite Ensembles." Thesis, Linköpings universitet, Matematisk statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-171096.

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In this thesis we present results about some eigenvalue statistics of the beta-Hermite ensembles, both in the classical cases corresponding to beta = 1, 2, 4, that is the Gaussian orthogonal ensemble (consisting of real symmetric matrices), the Gaussian unitary ensemble (consisting of complex Hermitian matrices) and the Gaussian symplectic ensembles (consisting of quaternionic self-dual matrices) respectively. We also look at the less explored general beta-Hermite ensembles (consisting of real tridiagonal symmetric matrices). Specifically we look at the empirical distribution function and two different scalings of the largest eigenvalue. The results we present relating to these statistics are the convergence of the empirical distribution function to the semicircle law, the convergence of the scaled largest eigenvalue to the Tracy-Widom distributions, and with a different scaling, the convergence of the largest eigenvalue to 1. We also use simulations to illustrate these results. For the Gaussian unitary ensemble, we present an expression for its level density. To aid in understanding the Gaussian symplectic ensemble we present properties of the eigenvalues of quaternionic matrices. Finally, we prove a theorem about the symmetry of the order statistic of the eigenvalues of the beta-Hermite ensembles.<br>I denna kandidatuppsats presenterar vi resultat om några olika egenvärdens-statistikor från beta-Hermite ensemblerna, först i de klassiska fallen då beta = 1, 2, 4, det vill säga den gaussiska ortogonala ensemblen (bestående av reella symmetriska matriser), den gaussiska unitära ensemblen (bestående av komplexa hermitiska matriser) och den gaussiska symplektiska ensemblen (bestående av kvaternioniska själv-duala matriser). Vi tittar även på de mindre undersökta generella beta-Hermite ensemblerna (bestående av reella symmetriska tridiagonala matriser). Specifikt tittar vi på den empiriska fördelningsfunktionen och två olika normeringar av det största egenvärdet. De resultat vi presenterar för dessa statistikor är den empiriska fördelningsfunktionens konvergens mot halvcirkel-fördelningen, det normerade största egenvärdets konvergens mot Tracy-Widom fördelningen, och, med en annan normering, största egenvärdets konvergens mot 1. Vi illustrerar även dessa resultat med hjälp av simuleringar. För den gaussiska unitära ensemblen presenterar vi ett uttryck för dess nivåtäthet. För att underlätta förståelsen av den gaussiska symplektiska ensemblen presenterar vi egenskaper hos egenvärdena av kvaternioniska matriser. Slutligen bevisar vi en sats om symmetrin hos ordningsstatistikan av egenvärdena av beta-Hermite ensemblerna.

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Obrist, Dominik. "On the stability of the swept leading-edge boundary layer /." Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/6767.

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Books on the topic "Hermite's Polynomial"

1

Baroudi, Djebar. Piecewise least squares fitting technique using finite interval method with Hermite polynomials. Technical Research Centre of Finland, 1993.

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2

Dyson, Freeman. Spectral statistics of unitary ensembles. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.4.

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This article focuses on the use of the orthogonal polynomial method for computing correlation functions, cluster functions, gap probability, Janossy density, and spacing distributions for the eigenvalues of matrix ensembles with unitary-invariant probability law. It first considers the classical families of orthogonal polynomials (Hermite, Laguerre, and Jacobi) and some corresponding unitary ensembles before discussing the statistical properties of N-tuples of real numbers. It then reviews the definitions of basic statistical quantities and demonstrates how their distributions can be made explicit in terms of orthogonal polynomials. It also describes the k-point correlation function, Fredholm determinants of finite-rank kernels, and resolvent kernels.

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Tavares, Santiago Alves. Generation of Multivariate Hermite Interpolating Polynomials. Taylor & Francis Group, 2019.

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Tavares, Santiago Alves. Generation of Multivariate Hermite Interpolating Polynomials. Taylor & Francis Group, 2005.

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5

Generation of multivariate hermite interpolating polynomials. Chapman & Hall/CRC, 2006.

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Tavares, Santiago Alves. Generation of Multivariate Hermite Interpolating Polynomials. Taylor & Francis Group, 2005.

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Anderson, Greg W. Spectral statistics of orthogonal and symplectic ensembles. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.5.

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This article describes a direct approach for computing scalar and matrix kernels, respectively for the unitary ensembles on the one hand and the orthogonal and symplectic ensembles on the other hand, leading to correlation functions and gap probabilities. In the classical orthogonal polynomials (Hermite, Laguerre, and Jacobi), the matrix kernels for the orthogonal and symplectic ensemble are expressed in terms of the scalar kernel for the unitary case, using the relation between the classical orthogonal polynomials going with the unitary ensembles and the skew-orthogonal polynomials going with the orthogonal and symplectic ensembles. The article states the fundamental theorem relating the orthonormal and skew-orthonormal polynomials that enter into the Christoffel-Darboux kernels

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Gusev, Alexander A., Galmandakh Chuluunbaatar, Ochbadrakh Chuluunbaatar, et al. Hermite interpolation polynomials on parallelepipeds and FEM applications. Vytautas Magnus University, 2023. http://dx.doi.org/10.7220/20.500.12259/258744.

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Tavares, Santiago Alves. Generation of Multivariate Hermite Interpolating Polynomials. Pure and Applied Mathematics. Taylor & Francis Group, 2006.

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Tavares, Santiago Alves. Generation of Multivariate Hermite Interpolating Polynomials (Pure and Applied Mathematics). Chapman & Hall/CRC, 2005.

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Book chapters on the topic "Hermite's Polynomial"

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Akhmedova, Valeriya, and Emil T. Akhmedov. "Hermite Polynomials." In SpringerBriefs in Physics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-35089-5_4.

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Koranga, Bipin Singh, Sanjay Kumar Padaliya, and Vivek Kumar Nautiyal. "Hermite Polynomials." In Special Functions and their Application. River Publishers, 2022. http://dx.doi.org/10.1201/9781003339595-5.

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Schweizer, Wolfgang. "Hermite Polynomials." In Special Functions in Physics with MATLAB. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-64232-7_16.

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Agarwal, Ravi P., and Patricia J. Y. Wong. "Hermite Interpolation." In Error Inequalities in Polynomial Interpolation and Their Applications. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2026-5_2.

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Aptekarev, A. I., and Herbert Stahl. "Asymptotics of Hermite-Padé Polynomials." In Progress in Approximation Theory. Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-2966-7_6.

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Wackernagel, Hans. "Gaussian Anamorphosis with Hermite Polynomials." In Multivariate Geostatistics. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05294-5_33.

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Hounkonnou, Mahouton Norbert. "( ℛ , p , q ) $$( \mathcal {R}, p,q)$$ -Rogers–Szegö and Hermite Polynomials, and Induced Deformed Quantum Algebras." In Orthogonal Polynomials. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36744-2_16.

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Zhang, Yunong, Dechao Chen, and Chengxu Ye. "Multi-Input Hermite-Polynomial WASD Neuronet." In Toward Deep Neural Networks. Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9780429426445-11.

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Driver, K. A., D. S. Lubinsky, and H. Wallin. "Hermite-Padé Polynomials and Approximation Properties." In Nonlinear Numerical Methods and Rational Approximation II. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0970-3_22.

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Oldham, Keith B., Jan C. Myland, and Jerome Spanier. "The Hermite Polynomials H n (x)." In An Atlas of Functions. Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-48807-3_25.

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Conference papers on the topic "Hermite's Polynomial"

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Tseng, Chien-Cheng, and Su-Ling Lee. "Computing Graph Fourier Transform Centrality with Graph Filter Designed by Hermite Polynomial." In 2024 International Conference on Consumer Electronics - Taiwan (ICCE-Taiwan). IEEE, 2024. http://dx.doi.org/10.1109/icce-taiwan62264.2024.10674625.

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Tseng, Chien-Cheng, and Su-Ling Lee. "Design of Hermite Polynomial Graph Filter and Its Application to Sensor Network Data Denoising." In 2024 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS). IEEE, 2024. https://doi.org/10.1109/apccas62602.2024.10808232.

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Kaltofen, Erich L. "Sparse Polynomial Hermite Interpolation." In ISSAC '22: International Symposium on Symbolic and Algebraic Computation. ACM, 2022. http://dx.doi.org/10.1145/3476446.3535501.

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Wu, Lin (Yuanbo), Deyin Liu, Xiaojie Guo, Richang Hong, Liangchen Liu, and Rui Zhang. "Multi-scale Spatial Representation Learning via Recursive Hermite Polynomial Networks." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/204.

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Multi-scale representation learning aims to leverage diverse features from different layers of Convolutional Neural Networks (CNNs) for boosting the feature robustness to scale variance. For dense prediction tasks, two key properties should be satisfied: the high spatial variance across convolutional layers, and the sub-scale granularity inside a convolutional layer for fine-grained features. To pursue the two properties, this paper proposes Recursive Hermite Polynomial Networks (RHP-Nets for short). The proposed RHP-Nets consist of two major components: 1) a dilated convolution to maintain the spatial resolution across layers, and 2) a family of Hermite polynomials over a subset of dilated grids, which recursively constructs sub-scale representations to avoid the artifacts caused by naively applying the dilation convolution. The resultant sub-scale granular features are fused via trainable Hermite coefficients to form the multi-resolution representations that can be fed into the next deeper layer, and thus allowing feature interchanging at all levels. Extensive experiments are conducted to demonstrate the efficacy of our design, and reveal its superiority over state-of-the-art alternatives on a variety of image recognition tasks. Besides, introspective studies are provided to further understand the properties of our method.

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Méhauté, Alain Le. "On Multivariate Hermite Polynomial Interpolation." In Proceedings of the International Workshop. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814503754_0010.

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Gaborit, Philippe, and Olivier Ruatta. "Improved Hermite multivariate polynomial interpolation." In 2006 IEEE International Symposium on Information Theory. IEEE, 2006. http://dx.doi.org/10.1109/isit.2006.261691.

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KURT, BURAK, and VELİ KURT. "HERMITE-BERNOULLI 2D POLYNOMIALS." In Proceedings of the 13th Regional Conference. World Scientific Publishing Company, 2012. http://dx.doi.org/10.1142/9789814417532_0004.

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Kauderer, Mark. "Modes in n-dimensional first-order systems." In OSA Annual Meeting. Optica Publishing Group, 1993. http://dx.doi.org/10.1364/oam.1993.thpp.1.

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The evolution of the Hermite–Gaussian modes in one dimensional centered nonlossless sytems is a well known result.1 Using the generalized Hermite polynomials used by Arnaud2 we can easily prove by induction the corresponding result for any finite dimensional first order system, including misalignment and the corresponding normalization terms. Phase conjugators are easily incorporated into the analysis. Various properties of the generalized Hermite polynomials are proved. Biorthogonality of the modes is demonstrated. The higher order modes are not periodic, i.e. they have no self consistent solutions except the separable one dimensional solutions. Some applications involving the Hermite–Gaussians are also presented.

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Gupta, Somit, and Arne Storjohann. "Computing hermite forms of polynomial matrices." In the 36th international symposium. ACM Press, 2011. http://dx.doi.org/10.1145/1993886.1993913.

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Cação, I., Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Monogenic Generalized Hermite Polynomials and Associated Hermite-Bessel Functions." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498033.

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Reports on the topic "Hermite's Polynomial"

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Herman, Martin, and Rama Chellappa. A reliable optical flow algorithm using 3-D hermite polynomials. National Institute of Standards and Technology, 1993. http://dx.doi.org/10.6028/nist.ir.5333.

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