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丛书名： SIAM Spotlights

2024年

作者： Gérard Meurant Petr Tichý

ISBN: (数字)9781611977868

ISBN: (纸本)9781611977851

The conjugate gradient (CG) algorithm is almost always the iterative method of choice for solving linear systems with symmetric positive definite matrices. This book describes and analyzes techniques based on Gauss quadrature rules to cheaply compute bounds on norms of the error. The techniques can be used to derive reliable stopping criteria. Computation of estimates of the smallest and largest eigenvalues during CG iterations is also shown. The algorithms are illustrated by many numerical experiments, and they can be easily incorporated into existing CG codes.

关键词： conjugate gradient algorithm linear system of equations error norms bounds of error norms eigenvalues Gauss quadrature rule Gauss-Radau quadrature rule tridiagonal matrices adaptive algorithms

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Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization (vol 22, pg 561, 2007)

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OPTIMIZATION METHODS & SOFTWARE 2013年第1期28卷 217-219页

作者： Babaie-Kafaki, Saman Semnan Univ Fac Math Stat & Comp Sci Dept Math Semnan Iran Inst Res Fundamental Sci IPM Sch Math Tehran Iran

In Andrei [Scaled memoryless BFGS preconditioned conjugate gradient (CG) algorithm for unconstrained optimization, Optim. Meth. Softw. 22(4) (2007), pp. 561-571], an efficient CG algorithm has been proposed for solving unconstrained optimization problems. However, due to a wrong inequality used in Andrei to show the sufficient descent property for the search directions, the proof of Theorem 2, the global convergence theorem, is incorrect. In what follows, the necessary corrections will be mentioned. Throughout, we use the same notations as in Andrei.

关键词： conjugate gradient algorithm sufficient descent condition line search global convergence

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Simulation of Electrical Circuits Using conjugate gradient algorithm

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Procedia Engineering 2015年 129卷 308-316页

作者： Y.A. Burtsev Platov South-Russian State Polytechnic University (NPI) 132 St. Prosvescheniya Rostov region Novocherkassk 346428 Russian Federation

Problems of electrical circuits’ simulation are known for a long time. However, the simulation quality and speed are far from perfect, especially when it comes to non-linear circuits. The method offered is based on table form of electrical circuits’ equations. Differential-algebraic equations of electrical circuits are converted to the systems of linear algebraic equations (SLAE) with finite differences method. It is important that SLAE are solved with conjugate gradient algorithm (CGA) that is well adapted to systems with sparse matrixes. The solution of the SLAE at previous time step is a good initial approximation of the solution at present time step. That is why CGA reduces calculations to 20-40% of the full algorithm typically. The possibility of using CGA for solving SLAE with matrixes that have no specific sign is proved by numerical experiments. A method for acceleration of solving electrical circuits’ SLAE is proposed. It differs from the Nodal Voltages Method as no apparent avatar of circuit SLAE is formed. A comparison of program “Electroscope” based on proposed method with programs “PSIM” and “Fastmean” is presented. “Electroscope” is leading in terms of quality and speed of test circuits’ simulations.

关键词： Electrical circuits simulation table form of equations conjugate gradient algorithm matrixes with no specific sign simulation speed reliability comparing.

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A Hybrid conjugate gradient algorithm for Solving Relative Orientation of Big Rotation Angle Stereo Pair

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Journal of Geodesy and Geoinformation Science 2020年第2期3卷 62-70页

作者： Jiatian LI Congcong WANG Chenglin JIA Yiru NIU Yu WANG Wenjing ZHANG Huajing WU Jian LI Faculty of Land Resource Engineering Kunming University of Science and TechnologyKunming 650093China Surveying and Mapping Geo-Informatics Technology Research Center Plateau Mountains of Yunnan Higher Education of Kunming University of Science and TechnologyKunming 650093China

The fast convergence without initial value dependence is the key to solving large angle relative ***,a hybrid conjugate gradient algorithm is proposed in this *** concrete process is:①stochastic hill climbing(SHC)algorithm is used to make a random disturbance to the given initial value of the relative orientation element,and the new value to guarantee the optimization direction is generated.②In local optimization,a super-linear convergent conjugate gradient method is used to replace the steepest descent method in relative orientation to improve its convergence rate.③The global convergence condition is that the calculation error is less than the prescribed limit *** comparison experiment shows that the method proposed in this paper is independent of the initial value,and has higher accuracy and fewer iterations.

关键词： relative orientation big rotation angle global convergence stochastic hill climbing conjugate gradient algorithm

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Signal reconstruction by conjugate gradient algorithm based on smoothing l1-norm

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CALCOLO 2019年第4期56卷 1页

作者： Wu, Caiying Zhan, Jiaming Lu, Yue Chen, Jein-Shan Inner Mongolia Univ Coll Math Sci Hohhot 010021 Peoples R China Tianjin Normal Univ Sch Math Sci Tianjin 300387 Peoples R China Natl Taiwan Normal Univ Dept Math Taipei 11677 Taiwan

The l(1)-norm regularized minimization problem is a non-differentiable problem and has a wide range of applications in the field of compressive sensing. Many approaches have been proposed in the literature. Among them, smoothing l(1)-norm is one of the effective approaches. This paper follows this path, in which we adopt six smoothing functions to approximate the l(1)-norm. Then, we recast the signal recovery problem as a smoothing penalized least squares optimization problem, and apply the nonlinear conjugate gradient method to solve the smoothing model. The algorithm is shown globally convergent. In addition, the simulation results not only suggest some nice smoothing functions, but also show that the proposed algorithm is competitive in view of relative error.

关键词： l(1)-norm regularization Compressive sensing conjugate gradient algorithm Smoothing function

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Set-membership constrained conjugate gradient adaptive algorithm for beamforming

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IET SIGNAL PROCESSING 2012年第8期6卷 789-797页

作者： Wang, L. de Lamare, R. C. China Unicom Res Inst Mkt & Management Res Ctr Beijing 100032 Peoples R China Univ York Dept Elect Commun Res Grp York YO10 5DD N Yorkshire England

In this work, a constrained adaptive filtering strategy based on conjugate gradient (CG) and set-membership techniques is presented for adaptive beamforming. A constraint on the magnitude of the array output is imposed to derive an adaptive algorithm that performs data-selective updates when calculating the beamformer's parameters. A linearly constrained minimum variance optimisation problem is consider with the bounded constraint based on this strategy and propose a CG-type algorithm for implementation. The proposed algorithm has data-selective updates, a variable forgetting factor and performs one iteration per update to reduce the computational complexity. The updated parameters construct a space of feasible solutions that enforce the constraints. The authors also introduce two time-varying bounding schemes to measure the quality of the parameters that could be included in the parameter space. A comprehensive complexity and performance analysis between the proposed and existing algorithms are provided. Simulations are performed to show the enhanced convergence and tracking performance of the proposed algorithm as compared with existing techniques.

关键词： parameter space adaptive filters comprehensive complexity parameter quality measurement iteration method Optimisation techniques linear programming conjugate gradient algorithm constraint theory set membership constrained technique performance analysis adaptive beamforming Filtering methods in signal processing time-varying bounding scheme Signal processing theory bounded constraint array signal processing convergence Interpolation and function approximation (numerical analysis) conjugate gradient methods constrained adaptive filtering strategy linear constrained minimum variance optimisation

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A conjugate gradient-based algorithm for large-scale quadratic programming problem with one quadratic constraint

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2019年第1期74卷 195-223页

作者： Taati, A. Salahi, M. Univ Guilan Fac Math Sci Rasht Iran

In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the sparsity of the involved matrices and solves the problem via solving a sequence of positive definite system of linear equations after identifying suitable generalized eigenvalues. Specifically, we analyze how to recognize hard case (case 2) in a preprocessing step, fixing an error in Sect.2.2.2 of Pong and Wolkowicz (Comput Optim Appl 58(2):273-322, 2014) which studies the same problem with the two-sided constraint. Some numerical experiments are given to show the effectiveness of the proposed method and to compare it with some recent algorithms in the literature.

关键词： QCQP conjugate gradient algorithm Generalized eigenvalue problem

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NON-UNITARY JOINT ZERO-BLOCK DIAGONALIZATION OF MATRICES USING A conjugate gradient algorithm

NON-UNITARY JOINT ZERO-BLOCK DIAGONALIZATION OF MATRICES USI...

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European Signal Processing Conference

作者： O. Cherrak H. Ghennioui E. H. Abarkan N. Thirion-Moreau E. Moreau Universite Sidi Mohamed Ben Abdellah FSTF LSSC Faculte des Sciences et Techniques de Fes Universite de Toulon CNRS LSIS UMR 7296

ISBN: (纸本)9781479988518

This communication addresses a new problem which is the Non-Unitary Joint Zero-Block Diagonalization of a given set of complex matrices. This problem can occur in fields of applications such as blind separation of convolutive mixtures of sources and generalizes the non unitary Joint Zero-Diagonalization problem. We present a new method based on the conjugate gradient algorithm. Our algorithm uses a numerical diagram of optimization which requires the calculation of the complex gradient matrix. The main advantages of the proposed method stem from the conjugate gradient properties: it is fast, stable and robust. Computer simulations are provided in order to illustrate the good behavior of the proposed method in different contexts. Two cases are studied: in the first scenario, a set of exactly zero-block-diagonal matrices are considered, then these matrices are progressively perturbed by an additive gaussian noise.

关键词： Joint zero-block diagonalization Matrix decompositions conjugate gradient algorithm Linear convolutive mixtures matrices conjugate gradient matrix decomposition dies Joints algorithms Computer Simulation conjugates complex gradient

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Erratum to: Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization

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Optimization Methods & Software 2013年第1期28卷 217页

作者： Babaie-Kafaki, Saman [a] Department of Mathematics Faculty of Mathematics Statistics and Computer Sciences Semnan University PO Box 35195-363 Semnan Iran [b] School of Mathematics Institute for Research in Fundamental Sciences (IPM) PO Box 19395-5746 Tehran Iran

关键词： conjugate gradient algorithm sufficient descent condition line search global convergence

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Smoothing Strategy Along with conjugate gradient algorithm for Signal Reconstruction

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JOURNAL OF SCIENTIFIC COMPUTING 2021年第1期87卷 21-21页

作者： Wu, Caiying Wang, Jing Alcantara, Jan Harold Chen, Jein-Shan Inner Mongolia Univ Coll Math Sci Hohhot 010021 Peoples R China Natl Taiwan Normal Univ Dept Math Taipei 11677 Taiwan De La Salle Univ Math & Stat Dept Manila 1004 Philippines

In this paper, we propose a new smoothing strategy along with conjugate gradient algorithm for the signal reconstruction problem. Theoretically, the proposed conjugate gradient algorithm along with the smoothing functions for the absolute value function is shown to possess some nice properties which guarantee global convergence. Numerical experiments and comparisons suggest that the proposed algorithm is an efficient approach for sparse recovery. Moreover, we demonstrate that the approach has some advantages over some existing solvers for the signal reconstruction problem.

关键词： lp-norm regularization Signal recovery conjugate gradient algorithm Sparse solution 90C33

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