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Frequency Analysis of recurrence Variational P-Splines

OPTOELECTRONICS INSTRUMENTATION AND DATA PROCESSING 2017年第6期53卷 591-598页

作者： Kochegurova, E. A. Kochegurov, A. I. Rozhkova, N. E. Tomsk Polytech Univ Pr Lenina 30 Tomsk 634050 Russia

Frequency responses of the procedure of spline-smoothing of information coming in real time are obtained. A recurrence spline is studied from the standpoint of the theory of linear dynamical systems. The estimation of quality and sustainability of the recurrence spline filter are described. The spline conversion laws identified in a frequency analysis are confirmed by the indicators of smoothing quality in the time domain.

关键词： recurrence algorithm spline filter free spline variational spline system function hardware function

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Construction and Optimization of Predictions on the Basis of First-Degree recurrence Splines

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NUMERICAL ANALYSIS AND APPLICATIONS 2010年第2期3卷 186-198页

作者： Shumilov, B. M. Esharov, E. A. Arkabaev, N. K. Tomsk State Univ Architecture & Civil Engn Pl Solyanaya 2 Tomsk 634003 Russia Tomsk State Univ Tomsk 634050 Russia Osh State Univ Osh 723520 Kyrgyzstan

The problem of point and interval predictions of time series on the basis of first-degree recurrence splines with depth 1 is investigated. Optimality conditions for the coefficients of the calculation formula are found. Results of numerical experiments for analytically given functions with errors are presented. A comparison with classical methods of prediction of time series is given.

关键词： spline recurrence algorithm optimization prediction time series

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On the recursive and explicit form of the general JCP Miller formula with applications

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ADVANCES IN APPLIED MATHEMATICS 2024年 156卷

作者： Bugajewski, Dariusz Bugajewski, Dawid Gan, Xiao-Xiong Mackowiak, Piotr Adam Mickiewicz Univ Fac Math & Comp Sci Dept Nonlinear Anal & Appl Topol Uniwersytetu Poznanskiego 4 PL-61614 Poznan Poland Univ Warsaw Fac Phys Pasteura 5 PL-02093 Warsaw Poland Morgan State Univ Dept Math Baltimore MD 21251 USA

The famous J.C.P. Miller formula provides a recurrence algorithm for the composition B a degrees f , where B a is the formal binomial series and f is a formal power series, however it requires that f has to be a nonunit. In this paper we provide the general J.C.P. Miller formula which eliminates the requirement of nonunitness of f and, instead, we establish a necessary and sufficient condition for the existence of the composition B a degrees f . We also provide the general J.C.P. Miller recurrence algorithm for computing the coefficients of that composition, if B a degrees f is well defined, obviously. Our generalizations cover both the case in which f is a one-variable formal power series and the case in which f is a multivariable formal power series. In the central part of this article we state, using some combinatorial techniques, the explicit form of the general J.C.P. Miller formula for one -variable case. As applications of these results we provide an explicit formula for the inverses of polynomials and formal power series for which the inverses exist, obviously. We also use our results to investigation of approximate solution to a differential equation which cannot be solved in an explicit way. (c) 2024 Elsevier Inc. All rights reserved.

关键词： Approximate solution Composition of formal power series Determinants Formal power series Hessenberg matrices Infinite matrices Initial value problem Inverses JCP Miller formula recurrence algorithm Separable equation Trudi formula

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Some computational aspects of Tchebichef moments for higher orders

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PATTERN RECOGNITION LETTERS 2018年第Sep.1期112卷 332-339页

作者： Camacho-Bello, Cesar Rivera-Lopez, Jose S. Univ Politecn Tulancingo Tulancingo Hidalgo Mexico

In this work, we propose a new algorithm for the computation of Tchebichef moments by means of a recurrence relation with respect to order and the Gram-Schmidt process, which reduces the numerical instability and the carry error caused by the computation of high-order moments. Results and comparison with other methods are presented. (c) 2018 Elsevier B.V. All rights reserved.

关键词： Discrete orthogonal polynomials Tchebichef polynomials Tchebichef moments recurrence algorithm Numerical propagations errors

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Efficient Hermite Spectral-Galerkin Methods for Nonlocal Diffusion Equations in Unbounded Domains

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Numerical Mathematics(Theory,Methods and Applications) 2022年第4期15卷 1009-1040页

作者： Huiyuan Li Ruiqing Liu Li-Lian Wang State Key Laboratory of Computer Science/Laboratory of Parallel Computing Institute of SoftwareChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100190China Division of Mathematical Sciences School of Physical and Mathematical SciencesNanyang Technological University637371Singapore

In this paper,we develop an efficient Hermite spectral-Galerkin method for nonlocal diffusion equations in unbounded *** show that the use of the Hermite basis can de-convolute the troublesome convolutional operations involved in the nonlocal *** a result,the“stiffness”matrix can be fast computed and assembled via the four-point stable recursive algorithm with O(N^(2))arithmetic ***,the singular factor in a typical kernel function can be fully absorbed by the *** the aid of Fourier analysis,we can prove the convergence of the *** demonstrate that the recursive computation of the entries of the stiffness matrix can be extended to the two-dimensional nonlocal Laplacian using the isotropic Hermite functions as basis *** provide ample numerical results to illustrate the accuracy and efficiency of the proposed algorithms.

关键词： Nonlocal diffusion equation spectral-Galerkin Hermite functions correlation/convolution recurrence algorithm

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New algorithms for Taylor coefficients of indefinite integrals and their applications

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APPLIED MATHEMATICS AND COMPUTATION 2014年 247卷 872-879页

作者： Chang, Shih-Hsiang Far East Univ Dept Mech Engn Tainan 74448 Taiwan

New recurrence algorithms for calculating the Taylor coefficients of indefinite integral are introduced and proved in this paper. These algorithms are simple in form, only involve the analytic operations: addition and multiplication, and can be directly implemented in any symbolic language. Also, no specific restriction on the kernel is required. Several types of Volterra equations such as integral, integro-differential and system of integro-differential equations with nondegenerate kernel are then solved to demonstrate the accuracy and efficiency of the proposed scheme. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Taylor series method Volterra integral equation Volterra integro-differential equation recurrence algorithm

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On Computational Aspects of Tchebichef Polynomials for Higher Polynomial Order

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IEEE ACCESS 2017年 5卷 2470-2478页

作者： Abdulhussan, Sadiz H. Ramli, Abd Rahman Al-Haddad, Syed Abdul Rahman Mahmmod, Basheera M. Jassim, Wissam A. Univ Putra Malaysia Dept Comp & Commun Syst Engn Serdang 43400 Malaysia Univ Dublin Trinity Coll Dublin ADAPT Ctr Sch Engn Dublin 2 Ireland Univ Baghdad Dept Comp Engn Baghdad 10071 Iraq

Tchebichef polynomials (TPs) and their moments are widely used in signal processing due to their remarkable performance in signal analysis, feature extraction, and compression capability. The common problem of the TP is that the coefficients computation is prone to numerical instabilities when the polynomial order becomes large. In this paper, a new algorithm is proposed to compute the TP coefficients (TPCs) for higher polynomial order by combining two existing recurrence algorithms: the three-term recurrence relations in the n-direction and x-direction. First, the TPCs are computed for x, n = 0, 1, ..., (N/2) - 1 using the recurrence in the x-direction. Second, the TPCs for x = 0, 1, ..., (N/2) - 1 and n = (N/2), (N/2) + 1,..., N - 1 based on n and x directions are calculated. Finally, the symmetry condition is applied to calculate the rest of the coefficients for x = (N/2), (N/2) + 1, ..., N - 1. In addition to the ability of the proposed algorithm to reduce the numerical propagation errors, it also accelerates the computational speed of the TPCs. The performance of the proposed algorithm was compared to that of existing algorithms for the reconstruction of speech and image signals taken from different databases. The performance of the TPCs computed by the proposed algorithm was also compared with the performance of the discrete cosine transform coefficients for speech compression systems. Different types of speech quality measures were used for evaluation. According to the results of the comparative analysis, the proposed algorithm makes the computation of the TP superior to that of conventional recurrence algorithms when the polynomial order is large.

关键词： Orthogonal polynomials recurrence algorithm Tchebichef polynomials numerical propagations errors

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ON THE SPECTRAL DYADIC GREEN-FUNCTION FOR STRATIFIED LINEAR MEDIA - APPLICATION TO MULTILAYER MIC LINES WITH ANISOTROPIC DIELECTRICS

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IEE PROCEEDINGS-H MICROWAVES ANTENNAS AND PROPAGATION 1987年第3期134卷 241-248页

作者： MARQUES, R HORNO, M Departamento de Electricidad y Electronica Facultad de Fisica Universidad de Sevilla Sevilla Spain

The problem of finding the spectral Green's dyadic matrix for planar stratified linear media, with layers of arbitrary electromagnetic properties and arbitrary current sources at interfaces, is solved in the spectral domain as a chain of 2- and single-layer problems. The main advantage of this method is that it transforms ann-layer problem inton2-layer stripline problems plus 2n(nfor lossless media) single-layer problems by using a recurrence algorithm, which is obtained here. The method can be applied to multiconductor and multilayer planar microwave integrated circuit (MIC) lines with anisotropic substrates. Explicit algorithms and numerical examples are provided.

关键词： microwave integrated circuits Waveguides and microwave transmission lines spectral dyadic Green's function strip lines anisotropic dielectrics arbitrary electromagnetic properties spectral domain arbitrary current sources stratified linear media recurrence algorithm Green's function methods planar microwave integrated circuit Waveguide and cavity theory waveguide theory multilayer MIC lines microstrip stripline problems Solid-state microwave circuits and devices

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Performance Analysis of M2M Traffic in LTE Network Using Queuing Systems with Random Resource Requirements

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AUTOMATIC CONTROL AND COMPUTER SCIENCES 2018年第5期52卷 345-353页

作者： Sopin, E. S. Ageev, K. A. Markova, E. V. Vikhrova, O. G. Gaidamaka, Yu. V. RUDN Univ Peoples Friendship Univ Russia Appl Probabil & Informat Dept Moscow 117198 Russia

We analyze a multiserver queuing system, in which customers require a server and a certain amount of limited resources for the duration of their service. For the case of discrete resources, we develop a recurrence algorithm to evaluate the model's stationary probability distribution and its various stationary characteristics, such as the blocking probability and the average amount of occupied resources. The algorithm is applied to analysis of M2M traffic characteristics in a LTE network cell. We derive the cumulative distribution function of radio resource requirements of M2M devices and propose a sampling approach in order to apply the recurrence algorithm to the case of continuous resources.

关键词： Queueing system limited resources random requirements recurrence algorithm normalization constant CDF approximation M2M LTE

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On the computational aspects of Charlier polynomials

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COGENT ENGINEERING 2020年第1期7卷 Article: 1763553页

作者： Abdul-Hadi, Alaa M. Abdulhussain, Sadiq H. Mahmmod, Basheera M. Univ Baghdad Dept Comp Engn Baghdad 10071 Iraq

Charlier polynomials (CHPs) and their moments are commonly used in image processing due to their salient performance in the analysis of signals and their capability in signal representation. The major issue of CHPs is the numerical instability of coefficients for high-order polynomials. In this study, a new recurrence algorithm is proposed to generate CHPs for high-order polynomials. First, sufficient initial values are obtained mathematically. Second, the reduced form of the recurrence algorithm is determined. Finally, a new symmetry relation for CHPs is realized to reduce the number of recurrence times. The symmetry relation is applied to calculate,50% of the polynomial coefficients. The performance of the proposed recurrence algorithm is evaluated in terms of computational cost and reconstruction error. The evaluation involves a comparison with existing recurrence algorithms. Moreover, the maximum size that can be generated using the proposed recurrence algorithm is investigated and compared with those of existing recurrence algorithms. Comparison results;indicate that the proposed algorithm exhibits better performance because it can generate a polynomial 44 times faster than existing recurrence algorithms. In addition, the improvement of the proposed

关键词： orthogonal polynomials Charlier polynomials Charlier moments recurrence algorithm

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