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Communications on Applied Mathematics and Computation 2022年第4期4卷 1313-1350页

作者： Ren-jun Qi Zhi-zhong Sun School of Mathematics Southeast UniversityNanjing 210096JiangsuChina

With the help of the asymptotic expansion for the classic Li formula and based on the L1-type compact difference scheme,we propose a temporal Richardson extrapolation method for the fractional sub-diffusion *** extrapolation formulas are presented,whose temporal convergence orders in L_(∞)-norm are proved to be 2,3-α,and 4-2α,respectively,where 0fast algorithm for Caputo fractional derivative based on the sum-of-exponential approximation,the fast extrapolation methods are obtained which reduce the computational complexity significantly while keep-ing the *** numerical experiments confirm the theoretical results.

关键词： L1 formula Asymptotic expansion Fractional sub-diffusion equation Fractional wave equation Richardson extrapolation fast algorithm

fast precise integration method for hyperbolic heat conduction problems

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Applied Mathematics and Mechanics(English Edition) 2013年第7期34卷 791-800页

作者：吴峰高强钟万勰 State Key Laboratory of Structural Analysis of Industrial Equipment Department of Engineering Mechanics Faculty of Vehicle Engineering and Mechanics Dalian University of Technology

A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suitable for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.

关键词： hyperbolic heat conduction sparse matrix precise integration method matrix exponential fast algorithm

fast Simulation of Lipid Vesicle Deformation Using Spherical Harmonic Approximation

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Communications in Computational Physics 2017年第1期21卷 40-64页

作者： Michael Mikucki Yongcheng Zhou Department of Applied Mathematics&Statistics Colorado School of MinesGoldenColorado80401USA Department of Mathematics Colorado State UniversityFort CollinsColorado80523USA

Lipid vesicles appear ubiquitously in biological *** how the mechanical and intermolecular interactions deform vesicle membranes is a fundamental question in *** this article we develop a fast algorithm to compute the surface configurations of lipid vesicles by introducing surface harmonic functions to approximate themembrane *** parameterization allows an analytical computation of themembrane curvature energy and its gradient for the efficient minimization of the curvature energy using a nonlinear conjugate gradient *** approach drastically reduces the degrees of freedom for approximating the membrane surfaces compared to the previously developed finite element and finite difference *** deformations with a reduced volume larger than 0.65 can be well approximated by using as small as 49 surface harmonic *** method thus has a great potential to reduce the computational expense of tracking multiple vesicles which deform for their interaction with external fields.

关键词： Lipid bilayer curvature energy surface harmonics fast algorithm

A fast Super-Resolution Reconstruction from Image Sequence

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Wuhan University Journal of Natural Sciences 2006年第2期11卷 399-404页

作者： SHI Wenzhong TIAN Yan LIU Jian Department of Land Surveying and Geo-Informatics The Hong Kong Polytechnic University Hong Kong China Department of Electronic and Information Engineering Huazhong University of Science and Technology Wuhan 430074 Hubei China

Based on the mechanism of imagery, a novel method called the delaminating combining template method, used for the problem of super-resolution reconstruction from image sequence, is described in this paper. The combining template method contains two steps： a delaminating strategy and a combining template algorithm. The delaminating strategy divides the original problem into several sub-problems; each of them is only eonnected to one degrading factor. The combining template algorithm is suggested to resolve each sub-problem. In addition, to verify the valid of the method, a new index called oriental entropy is presented. The results from the theoretical analysis and experiments illustrate that this method to be promising and efficient.

关键词： super-resolution technique fast algorithm oriental entropy combining template

High-precision,fast DEM reconstruction method for spaceborne InSAR

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Science China(Information Sciences) 2011年第11期54卷 2400-2410页

作者： WANG QingSong,HUANG HaiFeng,DONG Zhen,YU AnXi & LIANG DianNong National University of Defense Technology,Changsha 410073,China National University of Defense Technology Changsha China

The primary objective of the spaceborne interferometric synthetic aperture radar (InSAR) system is to develop a consistent global digital elevation model (DEM).The improvement of the processing speed in global interferometry missions while maintaining the accuracy is becoming an important *** reconstruction is the most time-consuming step in the data processing required for spaceborne *** on a DEM reconstruction principle analysis,we exploited two basic characteristics of the mapping relation between the interferometric phase and 3-D position of target ***,the relation between the 3-D position of the target point and the interferometric phase can be approximated using ***,the corresponding polynomials change slowly in the local SAR ***,we verified the foundations of the two mentioned characteristics ***,we proposed a fast method of DEM reconstruction based on this *** descriptions of the step and key parameters of the fast algorithm are ***,the repeat-pass interferometric data obtained using TerraSAR-X was used to test the presented *** experimental results showed that a significant reduction in computation time is achieved with only a small loss in *** effectiveness and correctness of the proposed method were also validated.

关键词： interferometric synthetic aperture radar (InSAR) spaceborne SAR DEM reconstruction fast algorithm

A fast State-Based Peridynamic Numerical Model

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Communications in Computational Physics 2020年第1期27卷 274-291页

作者： Ning Du Xu Guo Hong Wang School of Mathematics Shandong UniversityJinan 250100China Department of Mathematics The Chinese University of Hong KongShatinN.T.Hong Kong Department of Mathematics University of South CarolinaSCUSA

The peridynamic(PD)theory is a reformulation of the classical theory of continuum solid mechanics and is particularly suitable for the representation of discontinuities in displacement fields and the description of cracks and their evolution in materials,which the classical partial differential equation(PDE)models tend to fail to ***,the PD models yield numerical methods with dense stiffness matrices which requires O(N^(2))memory and O(N^(3))computational complexity where N is the number of spatial ***,the PD models are deemed to be computationally very expensive especially for problems in multiple space ***-based PD models,which were developed lately,can be treated as a great improvement of the previous bond-based PD *** state-based PD models have more complicated structures than the bond-based PD *** this paper we develop a fast collocation method for a state-based linear PD model by exploring the structure of the stiffness matrix of the numerical *** method has an O(N)memory requirement and computational complexity of O(N log N)per Krylov sub-space *** methods are presented to show the utility of the method.

关键词： State-based peridynamic model fast algorithm collocation method stiffness matrix

fast Wavelet Transform for Toeplitz Matrices and Property Analysis

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Acta Mathematicae Applicatae Sinica 2005年第3期21卷 459-468页

作者： Hong-xia Wang Li-zhi Cheng Department of Mathematics & System Science National University of Defense Technology Changsha 410073China

fast wavelet transform algorithms for Toeplitz matrices are proposed in this paper. Distinctive from the well known discrete trigonometric transforms, such as the discrete cosine transform （DCT） and the discrete Fourier transform （DFT） for Toeplitz matrices, the new algorithms are achieved by compactly supported wavelet that preserve the character of a Toeplitz matrix after transform, which is quite useful in many applications involving a Toeplitz matrix. Results of numerical experiments show that the proposed method has good compression performance similar to using wavelet in the digital image coding. Since the proposed algorithms turn a dense Toeplitz matrix into a band-limited form, the arithmetic operations required by the new algorithms are O（N） that are reduced greatly compared with O（N log N） by the classical trigonometric transforms.

关键词： Wavelet transform Tocplitz matrix fast algorithm

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求解广义范德蒙矩阵逆矩阵的有效快速算法

高等学校计算数学学报 2011年第4期33卷 312-318页

作者：赵良东徐仲陆全西北工业大学应用数学系

An efficient and fast algorithm for the inverse of generalized Vandermonde matrix is *** examples show that a proper selected auxiliary knot makes our algorithm higher in precision than the algorithms by using the Gua... 详细信息

关键词： Vandermonde matrix generalized Vandermonde matrix inverse fast algorithm

Structured dark-field imaging for single nano-particles

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Chinese Physics B 2015年第8期24卷 497-500页

作者：陈健高昆王志立云文兵吴自玉 National Synchrotron Radiation Laboratory University of Science and Technology of China 5750 Imhoff Road ConcordCA94520 USA Institute of High Energy Physics Chinese Academy of Sciences

In this work, we extensively describe and demonstrate the structured dark-field imaging(SDFI). SDFI is a newly proposed x-ray microscopy designed for revealing the fine features below Rayleigh resolution, in which different orders of scattered x-ray photons are collected by changing the numerical aperture of the condenser. Here, the samples of single particles are discussed to extend the scope of the SDFI technique reported in a previous work(Chen J, Gao K, Ge X, et al.2013 Opt. Lett. 38 2068). In addition, the details of the newly invented algorithm are explained, which is able to calculate the intensity of any pixel on the image plane rapidly and reliably.

关键词： x-ray microscopy Rayleigh resolution fast algorithm

An Efficient Computational Method for Solving Nonlinear Matrix Equation and Its Application in Queuing Analysis

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Journal of Computer Science & Technology 1996年第3期11卷 272-285页

作者：黄骏朱涛 DepartmentofElectrical＆ComputerEngineeringConcordiaUniversity 1455deMaisonneuveBlvd.W.MontrealQuebec

The matrir analytic analysis of queues with complex arrival, vacation and service characteristics requires the solution of nonlinear matrir equation. The complexity and large dimensionality of the model require an efficient and smart algorithm for the so-lution. In this paperl we propose an efficient Adaptive Newton-Kantorovich (ANK)method for speeding up the algorithm solving the nonlinear matrir equation which is an inevitable step in the analysis of the queue with embedded Markov chain such as BMAP/SMSP/1/ queue or its discrete version. BMAP/SMSP/1/ is a queu-ing model with a Semi Markov Service time Process (SMSP) and a Batch Markovian Arrival Process (BMAP). The numerical result is preselited for the discrete case of N-MMBP/D/1 queue which arises in analyzing traffic aspect of computer communica-tion network, where MMBP is Markov Modulated Bermoulli Process. The comparisons of Adaptive Newton-Kantorovich (ANK) with Modified NeWton-Kalltorovich (MNK)show that ANK saves 3o% of CPU time when the number of user N is 50.

关键词： fast algorithm queuing model