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Biorthogonal Wavelet Construction Using homotopy method

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Chinese Journal of Electronics 2015年第4期24卷 772-775页

作者： ZHANG Shiqiang ZHANG Shufang WANG Yan Information Science and Technology College Dalian Maritime University

The biorthogonal wavelets families are used widely because they have compact support, complete symmetry and linear phase. According to B′ezout's theorem,the biorthogonal wavelets available now are only some particular examples of total solutions. The quantity of solutions is decided jointly by the scaling function vanishing moment N and dual vanishing moment N?. The relationship of N, N? and solutions' quantity is discussed in *** to the constraint conditions which the compact biorthogonal wavelets satisfy, a number of biorthogonal wavelets are constructed in which the global convergent homotopy method is used for different N and N?. The filter coefficients and plots of scaling function, dual scaling function, wavelet function and dual wavelet function are given.

关键词： Biorthonoral wavelet homotopy method Nonlinear equations

Iteratively weighted thresholding homotopy method for the sparse solution of underdetermined linear equations

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Science China Mathematics 2021年第3期64卷 639-664页

作者： Wenxing Zhu Zilin Huang Jianli Chen Zheng Peng Center for Discrete Mathematics and Theoretical Computer Science Fuzhou UniversityFuzhou 350116China

Recently, iteratively reweighted methods have attracted much interest in compressed sensing, outperforming their unweighted counterparts in most cases. In these methods, decision variables and weights are optimized alternatingly, or decision variables are optimized under heuristically chosen weights. In this paper,we present a novel weighted l1-norm minimization problem for the sparsest solution of underdetermined linear equations. We propose an iteratively weighted thresholding method for this problem, wherein decision variables and weights are optimized simultaneously. Furthermore, we prove that the iteration process will converge eventually. Using the homotopy technique, we enhance the performance of the iteratively weighted thresholding method. Finally, extensive computational experiments show that our method performs better in terms of both running time and recovery accuracy compared with some state-of-the-art methods.

关键词： sparse optimization weighted thresholding method homotopy method

A CONTINUATION homotopy method FOR THE INVERSE PROBLEM OF OPERATOR IDENTIFICATION AND ITS APPLICATION

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Applied Mathematics(A Journal of Chinese Universities) 1993年第1期8卷 69-75页

作者：韩波刘家琦卢惠林 Department of mathematics Harbin Institute of Technology Harbin 150006) Computer Application Development and Research Center of Heilonjiang Province Harbin

A new widly convergent method for solving the problem of operator identification is illustrated. Numerical simulations are carried out to test the feasibility and to study the general characteristics of the technique without the real measurement data. This technique is a direct application of the continuation homo-topy method for solving nonlinear systems of equations. It is found that this method does give excellent results in solving the inverse problem of the elliptic differential equations.

关键词： Inverse Problem homotopy method Elliptic Differential Equations.

Fault-tolerant decentralized H-infinity control for multi-channel systems using homotopy method

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控制理论与应用（英文版） 2007年第1期5卷 77-82页

作者： Ning CHEN Weihua GUI Masao IKEDA School of Information Science ＆ Engineering Central South University Changsha Hunan 410083 China Graduate School of Engineering Osaka University Suita Osaka 565-0871 Japan

This paper considers a fault-tolerant decentralized H-infinity control problem for multi-channel linear time-invariant systems. The purpose is to design a decentralized H-infinity output feedback controller *** the given system and achieve a certain H-infinity performance requirement both in the normal situation and in the situation where any one of the local controllers fails. The designed problem is reduced to a feasibility problem of a set of bilinear matrix inequalities （BMIs）. An algorithm is proposed to solve the BMIs. First, the normal situation is considered where all the local controllers are functioning. The local controllers are obtained from a standard centralized H-infinity controller by using a homotopy method imposing a structural constraint progressively. Secondly, the above case is extended to the one where any one of the local controllers fails. We again use a homotopy method where the coefficient matrices of the failed controller are decreased progressively to zero. The efficiency of the proposed algorithm is demonstrated by an example.

关键词： Decentralized control H-infinity control Fault-tolerant Control BMI homotopy method

Finding Periodic Solutions of High Order Duffing Equations via homotopy method

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Communications in Mathematical Research 2009年第3期25卷 193-203页

作者： YANG XUE Xu Xu College of Matheraatics Jilin University Changchun 130012

This paper presents a detailed analysis of finding the periodic solutions for the high order Duffing equation x^（2n）＋ g（x） = e（t）（n ≥ 1）. Firstly, we give a constructive proof for the existence of periodic solutions via the homotopy method. Then we establish an efficient and global convergence method to find periodic solutions numerically.

关键词： high order Duffing equation periodic solution homotopy method

A FINITE-DIFFERENCE RELAXATION SCHEME BASED ON BOTH MULTIGRID TECHNIQUES AND homotopy method FOR 2D STEADY-STATE NAVIER-STOKES EQUATIONS

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Journal of Hydrodynamics 1997年第1期9卷 42-55页

作者： Liao Shi-jun, Zhu Ji-maoDepartment of Naval Architecture & Ocean Engineering, Shanghai Jiao Tang University,Shanghai 200030, P. R. China

In this paper, multigrid techniques together with homotopy method are applied to propose a kind of finite-difference relaxation scheme for 2D steady-state Navier-Stokes equations. The proposed numerical scheme can give convergent results for viscous flows with high Reynolds number. As an example, the results of shear-driven cavity flow with high Reynolds number up to 25000 on fine grid 257×257 are given.

关键词： 2D Navier-Stokes equations multigrid techniques homotopy method shear-driven cavity flow

Parameter identification in reaction-diffusion models by homotopy method

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Parameter identification in reaction-diffusion models by hom...

Solving a Class of Brouwer Fixed-point Problems via a Modified Aggregate Constraint homotopy method

中国交叉科学学会第15届学术年会

作者：张文禹 Liu Bo 吉林大学数学研究所 School of Mathematics Jilin University

We consider certain one-dimensional reaction-diffusion models for two chemical substances with concentrations A（the reducing agent） and B（the coupler）.The reducing agent diffuses and combines with the *** the diffusion coefficient D（x） and the reaction rate k are *** that final time（t=T） measurements on A（x,T） and B（x,T） are given,the problem is therefore to identify D（x） and k.A homotopy method is proposed to allow us to identify these coefficients and some numerical experiments are made.

关键词： Parameter identification Reaction-diffusion equations homotopy method Numerical experiments

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Northeastern Mathematical Journal 2007年第5期23卷 377-385页

作者：苏孟龙吕显瑞 School of Mathematics Jilin University

In this paper, we provide an aggregate function homotopy interior point method to solve a class of Brouwer fixed-point problems. Compared with the homotopy method （proposed by Yu and Lin, Appl. Math. Comput., 74（1996）, 65）, the main adavantages of this method are as foUows： on the one hand, it can solve the Brouwer fixed-point problems in a broader class of nonconvex subsets Ω in R^n （in this paper, we let Ω={x∈ R^n ： gi（x） ≤0, i= 1,... , m}）; on the other hand, it can also deal with the subsets Ω with larger amount of constraints more effectively.

关键词： homotopy method Brouwer fixed-point problem nonconvex subset

Modified homotopy method for a Class of Brouwer Fixed-point Problems

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Northeastern Mathematical Journal 2007年第1期23卷 35-42页

作者：苏孟龙吕显瑞 School of Mathematics Jilin University Changchun 130012

In this paper, we modify the homotopy method （proposed by Yu and Lin, Appl. Math. Comput., 74（1996）, 65） and hence make the modified method be able to solve Brouwer fixed-point problems in a broader class of nonco... 详细信息

关键词： homotopy method Brouwer fixed-point problem nonconvex subset