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direct algorithm for computation of derivatives of the Daubechies basis functions

APPLIED MATHEMATICS AND COMPUTATION 2005年第2期170卷 1006-1013页

作者： Lin, WB Kovvali, N Carin, L Duke Univ Dept Elect & Comp Engn Durham NC 27708 USA

We extend the direct algorithm for computing the derivatives of the compactly supported Daubechies N-vanishing-moment basis functions. The method yields exact values at dyadic rationals for the nth derivative (0 <= n <= N - 1) of the basis functions, when it exists. Example results are shown for the first derivatives of the basis functions from the Daubechies N-vanishing-moment extremal phase orthonormal family (for N = 3,4, and 5), and the CDF(2, N) spline-based biorthogonal family (for N = 6,8 and 10). (c) 2005 Elsevier Inc. All rights reserved.

关键词： wavelets derivatives Daubechies basis functions cascade algorithm direct algorithm

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direct algorithm: A new definition of potentially optimal hyperrectangles

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APPLIED MATHEMATICS AND COMPUTATION 2006年第2期179卷 742-749页

作者： Chiter, Lakhdar Univ Setif Lab Math Fondamentales & Numer Setif 19000 Algeria

We propose a new version of potentially optimal intervals for the direct algorithm. A two-point based sampling method is presented. The method starts from a distinguished point (the peak point) by forming an initial triangle. The idea is to sample the midpoint of a specific interval: the basis of the resulting triangle. This specific interval is obtained by translating the initial interval towards the lowest function value: min {f(c(i)),f(c(i+1))} and then overcoming the disadvantage if the global minimum lies at the boundaries. Two-dimensional version of our subdivision and sampling method is also discussed. (c) 2005 Published by Elsevier Inc.

关键词： global optimization direct algorithm two-point based sampling method potentially optimal triangle

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direct algorithm for rectifying pairs of uncalibrated images

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ELECTRONICS LETTERS 2000年第5期36卷 419-420页

作者： Al-Shalfan, KA Haigh, JGB Ipson, SS Univ Bradford Dept Elect & Elect Engn Bradford BD7 1DP W Yorkshire England

Given the fundamental matrix connecting two uncalibrated images of a 3D scene, a convenient procedure is presented for determining transformations to make corresponding points lie on the same horizontal lines. The met... 详细信息

关键词： image processing Optical, image and video signal processing direct algorithm optical information processing fundamental matrix transformations calibration corresponding points rectification images uncalibrated images calibration cube rectifying pairs horizontal lines Measurement standards and calibration Image processing and restoration rectifying image pairs 3D scene

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direct algorithm for the solution of two-sided obstacle problems with M-matrix

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NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 2011年第1期18卷 167-173页

作者： Jiang, Ying-Jun Zeng, Jin-Ping Changsha Univ Sci & Technol Coll Math & Computat Sci Changsha 410004 Hunan Peoples R China Dongguan Univ Technol Coll Comp Dongguan 523005 Guangdong Peoples R China

A direct algorithm for the solution to the affine two-sided obstacle problem with an M-matrix is presented. The algorithm has the polynomial bounded computational complexity O(n(3)) and is more efficient than those in... 详细信息

关键词： two-sided obstacle problem direct algorithm M-matrix polynomial computational complexity

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direct algorithm FOR MAPPING LAND SURFACE FPAR FROM MODIS APPARENT REFLECTANCE AT TOP OF ATMOSPHERE

DIRECT ALGORITHM FOR MAPPING LAND SURFACE FPAR FROM MODIS AP...

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IEEE Joint International Geoscience and Remote Sensing Symposium (IGARSS) / 35th Canadian Symposium on Remote Sensing

作者： Liu, Rongyuan Ren, Huazhong Liu, Suhong Liu, Qiang Wang, Yuanyuan Beijing Normal Univ Sch Geog State Key Lab Remote Sensing Sci Beijing 100875 Peoples R China

ISBN: (纸本)9781479957750

Fraction of abstracted Photosynthetically Active Radiation (FPAR) is a fundamental terrestrial state variable in most ecosystem productivity models and is also one of the key terrestrial products. This paper proposed a new direct-algorithm to retrieve FPAR from apparent reflectance of MODIS's seven bands in the visible, near-infrared and short-wave wavelengths. The direct-algorithm developed from the dataset simulated by radiative transfer models of canopy and atmosphere with different canopy structures and atmosphere conditions, estimated direct FPAR (FPAR(dir)), and scattering FPAR (FPAR(set)), and total FPAR of the canopy (FPAR(tot)) by using linear equations of TOA reflectance. Result showed that the estimated FPAR product were close to that of MODIS products except the forest, perhaps because the homogenous canopy of the SAIL model is not suitable for the forest canopy.

关键词： FPAR MODIS direct algorithm TOA apparent reflectance

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Mrdirect: a multilevel robust direct algorithm for global optimization problems

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JOURNAL OF GLOBAL OPTIMIZATION 2015年第2期62卷 205-227页

作者： Liu, Qunfeng Zeng, Jinping Yang, Gang Dongguan Univ Technol Sch Comp Dongguan 523808 Peoples R China

Although direct global optimization algorithm quickly gets close to the basin of the optimum, it often takes much longer to refine the solution to a high degree of accuracy. This behavior of direct is similar to the "smooth mode phenomenon" encountered when solving linear systems discretized from partial differential equation (PDE). In the case of PDE, this smooth mode phenomenon can be eliminated efficiently by the multigrid algorithm in which the PDE solver is applied at different levels of discretization. In this paper we adapt the multigrid approach to a robust version of direct algorithm, obtaining a "multilevel" robust direct (Mrdirect) algorithm. Although additional parameters are needed, our numerical results show that Mrdirect is insensitive to the parameters, and the parameters setting proposed in this paper performs very well on the tested sets of benchmark problems, in terms of the speed with which the global optimum is found to a high degree of accuracy.

关键词： Global optimization Multilevel algorithm Multigrid algorithm direct algorithm Multilevel partition

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A new sampling method in the direct algorithm

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APPLIED MATHEMATICS AND COMPUTATION 2006年第1期175卷 297-306页

作者： Chiter, Lakhdar Setif Univ Dept Math Setif 19000 Algeria

Drawing inspiration from the fact that each point sampled by the direct algorithm will be a midpoint of the center subinterval, we present a one-dimensional version which considers two symmetric points, the one-third and two-third of the length of the considered interval. The center subinterval will be the region of interest. The interval is then bisected and two new points are added at every step. The two points sampled before became two-third and one-third, respectively. Two possibilities of definition of potentially optimal intervals are given. The proposed version predicts a fast convergence, and overcomes some disadvantages of the direct in the case where the global minimum lies at the boundaries. (c) 2005 Elsevier Inc. All rights reserved.

关键词： global optimization direct algorithm weakly optimal interval sampling method

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RESEARCH OF PROBLEMS ON REALIZING direct algorithm OF WAVELET TRANSFORM

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Chinese Journal of Mechanical Engineering 2003年第2期16卷 136-140页

作者： Tang BaopingZhong YoumingQin ShurenDepartment of Mechanical Engineering,Chongqing University,Chongqing 400044, China Department of Mechanical Engineering Chongqing University 重庆 400044

direct algorithm of wavelet transform (WT) is the numerical algorithmobtained from the integral formula of WT by directly digitization. Some problems on realizing thealgorithm are studied. Some conclusions on the direct algorithm of discrete wavelet transform (DWT),such as discrete convolution operation formula of wavelet coefficients and wavelet components,sampling principle and technology to wavelets, deciding method for scale range of wavelets, measuresto solve edge effect problem, etc, are obtained. The realization of direct algorithm of continuouswavelet transform (CWT) is also studied. The computing cost of direct algorithm and Mallat algorithmof DWT are still studied, and the computing formulae are obtained. These works are beneficial todeeply understand WT and Mallat algorithm. Examples in the end show that direct algorithm can alsobe applied widely.

关键词： wavelet transform direct algorithm mallat algorithm

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A direct algorithm Maple Package of One-Dimensional Optimal System for Group Invariant Solutions

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Communications in Theoretical Physics 2018年第1期69卷 14-22页

作者： Lin Zhang Zhong Han Yong Chen Shanghai Key Laboratory of Trustworthy Computing East China Normal UniversityShanghai 200062China Department of Physics Zhejiang Normal UniversityJinhua 321004China

To construct the one-dimensional optimal system of finite dimensional Lie algebra automatically,we develop a new Maple package One Optimal ***,we propose a new method to calculate the adjoint transformation matrix and find all the invariants of Lie algebra in spite of Killing form checking possible constraints of each ***,a new conception called invariance set is ***,this Maple package is proved to be more efficiency and precise than before by applying it to some classic examples.

关键词： symbolic computation mathematics mechanization direct algorithm optimal system

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A STUDY OF PARALLEL EFFICIENCY OF MODIFIED direct algorithm APPLIED TO THERMOHYDRODYNAMIC LUBRICATION

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JOURNAL OF MECHANICS 2009年第2期25卷 143-150页

作者： Wang, N. Tsai, C. -M. Cha, K. -C. Chang Gung Univ Dept Mech Engn Tao Yuan 33302 Taiwan

This study examines the parallel computing as a means to minimize the execution time ill the optimization applied to thermohydrodynamic (THD) lubrication. The objective of the optimization is to maximize the load capacity of a slider bearing with two design variables. A global optimization method, DIviding RECTangle (direct) algorithm, is used. The first approach was to apply the parallel computing within the THD model in a shared-memory processing (SMP) environment to examine the parallel efficiency of fine-grain computation. Next, a distributed parallel computing in the search level was conducted by use of the standard direct algorithm. Then, the algorithm is modified to provide a version suitable for effective parallel computing. Ill the latter coarse-grain computation the speedups obtained by the direct algorithms are compared with some previous Studies using other parallel optimization methods. In the fine-grain computation of the SMP machine, the communication and overhead time costs prohibit high speedup in the cases of four or more simultaneous threads. It is found that the standard direct algorithm is all efficient sequential but less parallel-computing-friendly method. When the modified algorithm is used in the slider bearing optimization, a parallel efficiency of 96.3% is obtained in the 16-computing-node cluster. This study presents the modified direct algorithm, in efficient parallel search method, for general engineering optimization problems.

关键词： Optimization Parallel computing Thermohydrodynamic lubrication direct algorithm

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