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modified conjugate gradient method for obtaining the minimum-norm solution of the generalized coupled Sylvester-conjugate matrix equations

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APPLIED MATHEMATICAL MODELLING 2016年第2期40卷 1260-1275页

作者： Huang, Na Ma, Chang-Feng Fujian Normal Univ Sch Math & Comp Sci Fuzhou 350007 Peoples R China

In this study, we consider the iteration solutions of the generalized coupled Sylvester-conjugate matrix equations: A(1)X + B1Y = D-1(X) over barE(1) +F-1, A(2)Y + B2X = D-2(Y) over barE(2) + F-2, where (X) over bar and (Y) over bar denote the conjugation of X and Y, respectively. We propose a modified conjugate gradient method and give the convergence analysis based on the premise that the coupled matrix equations are consistent. The convergence theorem shows that a solution (X*, Y*) can be obtained within finite iterative steps in the absence of round-off error for any initial value. Furthermore, we provide a method for choosing the initial matrices to obtain the minimum-norm solution of the problem. Finally, some numerical examples are given to demonstrate the behavior of the algorithms considered. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Generalized coupled Sylvester-conjugate matrix equations Minimum-norm solution modified conjugate gradient method Numerical experiment

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A modified conjugate gradient method for Transient Nonlinear Inverse Heat Conduction Problems: A Case Study for Identifying Temperature-Dependent Thermal Conductivities

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JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME 2014年第9期136卷 091301-1-091301-7页

作者： Cui, Miao Zhu, Qianghua Gao, Xiaowei Dalian Univ Technol Sch Aeronaut & Astronaut Fac Vehicle Engn & Mech State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China

Despite numerous studies of conjugate gradient methods (CGMs), the "sensitivity problem" and the "adjoint problem" are inevitable for nonlinear inverse heat conduction problems (IHCPs), which are accompanied by some assumptions and complicated differentiating processes. In this paper, a modified CGM (MCGM) is presented for the solution of a specified transient nonlinear IHCP, to recover temperature-dependent thermal conductivities for a case study. By introducing the complex-variable-differentiation method (CVDM) for sensitivity analysis, the sensitivity problem and the adjoint problem are circumvented. Five test examples are given to validate and assess the performance of the MCGM.

关键词： modified conjugate gradient method inverse problem transient nonlinear heat conduction complex-variable-differentiation method

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A new approach to speed up the conjugate gradient method by applying the complex variable differentiation method

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INVERSE PROBLEMS IN SCIENCE AND ENGINEERING 2019年第12期27卷 1703-1717页

作者： Farzan, Hadi Loulou, Tahar Sarvari, Seyed Masoud Hosseini Higher Educ Complex Bam Mech Engn Dept Bam 76615314 Iran Univ South Brittany IRDL Ctr Res Lorient France Shahid Bahonar Univ Kerman Mech Engn Dept Kerman Iran

This study represents a novel approach to speed up the solution of nonlinear inverse heat conduction problems (IHCPs) by the implementation of the complex variable differentiation method (CVDM). A difficulty appeared in the solution of nonlinear problems is the great amount of computational time. To handle this problem, a new scheme is introduced to improve the conjugate gradient method (CGM). The main contribution in the improvement of conventional CGM is the simultaneous solution of direct and sensitivity problems by applying the complex variable method. The derivation of sensitivity problem by utilizing the analytic derivative is difficult or impossible, since the direct problem is complicated mathematically in many cases. By this approach, the analytic derivation of sensitivity problem is circumvented, while the Jacobian matrix components are obtained accompanied by the solution of the direct problem. Therefore, the developed scheme results in the reduction of mathematical manipulations. Due to the high nonlinearity of moving boundary inverse problems, the ablation problem is considered as the benchmark to examine the accuracy and effectiveness of the proposed scheme. The simulated results illustrate that the developed scheme has the potential to significantly reducing of the computational expenses while maintaining the quality of numerical solution.

关键词： modified conjugate gradient method complex variable differentiation method sensitivity problem ablation problem nonlinear inverse problems

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The modified conjugate gradient methods for solving a class of generalized coupled Sylvester-transpose matrix equations

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2014年第8期67卷 1545-1558页

作者： Huang, Na Ma, Changfeng Fujian Normal Univ Sch Math & Comp Sci Fuzhou 350007 Peoples R China

In this paper, we consider the iteration solutions of generalized coupled Sylvestertranspose matrix equations: A(1)XB(1)+C-1 (YD1)-D-T = A(2)YB(2) + (C2XD2)-D-T = F-2. When the coupled matrix equations are consistent, we propose a modified conjugate gradient method to solve the equations and prove that a solution (X*, Y*) can be obtained within finite iterative steps in the absence of roundoff-error for any initial value. Furthermore, we show that the minimum-norm solution can be got by choosing a special kind of initial matrices. When the coupled matrix equations are inconsistent, we present another modified conjugate gradient method to find the least-squares solution with the minimum-norm. Finally, some numerical examples are given to show the behavior of the considered algorithms. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Generalized coupled Sylvester-transpose matrix equations modified conjugate gradient method Minimum-norm solution Least-squares solution Numerical experiment

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Minimum-norm Hamiltonian solutions of a class of generalized Sylvester-conjugate matrix equations

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2017年第5期73卷 747-764页

作者： Hu, Jing-Jing Ma, Chang-Feng Fujian Normal Univ Sch Math & Comp Sci Fuzhou 350117 Peoples R China Fujian Normal Univ FJKLMAA Fuzhou 350117 Peoples R China

In this study, we consider the iteration solutions of the generalized Sylvester-conjugate matrix equation: AXB + C (X) over barD = E by a modified conjugate gradient method. When the system is consistent, the convergence theorem shows that a solution can be obtained within finite iterative steps in the absence of round-off error for any initial value given Hamiltonian matrix. Furthermore, we can get the minimum-norm solution X* by choosing a special kind of initial matrix. Finally, some numerical examples are given to demonstrate the algorithm considered is quite effective in actual computation. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Generalized Sylvester-conjugate matrix equation modified conjugate gradient method Hamiltonian matrix Minimum-norm solution

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Reconstruction of the heat transfer coefficients and heat fluxes in heat conduction problems

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MATHEMATICS AND COMPUTERS IN SIMULATION 2021年 187卷 134-154页

作者： Abdelhamid, Talaat Elsheikh, Ammar H. Omisore, Olatunji Mumini Saeed, N. A. Muthuramalingam, T. Chen, Ronglinag Alam, Md. Mahbub Harbin Inst Technol Shenzhen Ctr Turbulence & Control Shenzhen 518055 Peoples R China Chinese Acad Sci Shenzhen Inst Adv Technol Shenzhen 518055 Peoples R China Menoufia Univ Dept Phys & Engn Math Fac Elect Engn Menoufia 32952 Egypt Tanta Univ Prod Engn & Mech Design Dept Fac Engn Tanta 31527 Egypt SRM Inst Sci & Technol Dept Mechatron Engn Kattankulathur Campus Chennai 603203 Tamil Nadu India

This paper studies the reconstruction of the spatial-dependent-heat transfer coefficient gamma(x) and- heat flux q(x), using the Levenberg-Marquardt (L-M) connected with the surrogate functional method and the modified conjugate gradient method (MCGM) (problem I). In addition to studying the reconstruction of gamma(x) and space-time-dependent heat flux q(x, t) using the MCGM (problem II). The numerical results obtained by the L-M and MCGM demonstrate the efficiency, accuracy, and robustness of the proposed methods. The obtained results are compared with those obtained from an inverse approach connected with COMSOL Multiphysics under the same conditions. Finally, a conclusion and some remarks are presented. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by ElsevierB.V. All rights reserved.

关键词： Simultaneous identification Numerical reconstruction Heat flux and heat transfer coefficient modified conjugate gradient method Levenberg-Marquardt method

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The iterative algorithm for solving a class of generalized coupled Sylvester-transpose equations over centrosymmetric or anti-centrosymmetric matrix

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2019年第8期96卷 1576-1594页

作者： Lv, Chang-Qing Ma, Chang-Feng Fujian Normal Univ Sch Math & Comp Sci Fuzhou 350117 Fujian Peoples R China Fujian Normal Univ FJKLMAA Fuzhou 350117 Fujian Peoples R China Zaozhuang Univ Sch Math & Stat Zaozhuang Peoples R China

In this paper, an iterative algorithm is presented for solving a class of generalized coupled Sylvester-transpose linear matrix equations over centrosymmetric or anti-centrosymmetric matrix. If the matrix equations are consistent, the solution through the iterative method can be obtained within finite steps without round-off error for any initial centrosymmentirc or anti-centrosymmetric value. Furthermore, one method is provided by choosing the special initial matrices to obtain the least norm solution. Finally, numerical examples are presented to demonstrate the efficiency of the algorithm we have proposed.

关键词： Generalized coupled Sylvester-transpose equations modified conjugate gradient method centrosymmetric or anti-centrosymmetric matrix least norm solution numerical experiment

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Simultaneous estimation of heat source strength of hot wire and thermal conductivity of material

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NUMERICAL HEAT TRANSFER PART A-APPLICATIONS 2024年

作者： Sathavara, Parth Parwani, Ajit Kumar Chaudhuri, Paritosh Inst Infrastruct Technol Res & Management Dept Mech & Aerosp Engn Ahmadabad India Inst Plasma Res Gandhinagar India Homi Bhabha Natl Inst HBNI Mumbai India Inst Infrastruct Technol Res & Management Dept Mech & Aerosp Engn Ahmadabad 380026 India

The hot-wire (HW) technique is a widely used method for measuring the thermal conductivity (k) of insulation materials. However, there are some limitations to the applicability. For instance, inaccuracies may arise when the wire is assumed to be infinitely thin and long, or when the sample material is assumed to be an infinite medium. Additionally, the accuracy of k measurements relies on accurately specifying the heat source strength (QW) generated by the HW. The modified conjugate gradient method (CGM) provides a solution to these limitations of the HW technique. In the modified CGM technique, a scaling factor based on the Levenberg-Marquardt method is utilized to address the low derivative and divergence issues of the traditional CGM. The current work simultaneously estimates QW generated by the HW and k of the sample materials by using modified CGM. The investigation looked into the effect of sensor positioning relative to the HW and the introduction of artificial Gaussian error (noise) with a standard deviation of 0.01 degrees C, 0.02 degrees C and 0.1 degrees C into the simulated temperature measurements. The modified CGM estimates the unknown parameters accurately compared to the traditional CGM. The measurement location should be closer to the HW to obtain accurate estimation results. The noise level of 0.1 degrees C results in low accuracy of estimation of k and QW for Plexiglas with one sensor, which can be enhanced by employing two sensors. Overall, the modified CGM algorithm proved to be a robust inverse algorithm that could be employed to estimate unknown parameters.

关键词： Heat source strength hot wire inverse heat transfer technique modified conjugate gradient method thermal conductivity

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Simultaneous reconstruction of the time-dependent Robin coefficient and heat flux in heat conduction problems

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INVERSE PROBLEMS IN SCIENCE AND ENGINEERING 2018年第9期26卷 1231-1248页

作者： Abdelhamid, Talaat Elsheikh, A. H. Elazab, Ahmed Sharshir, S. W. Selima, Ehab S. Jiang, Daijun Menoufiya Univ Phys & Math Engn Dept Fac Elect Engn Menoufia Egypt Chinese Acad Sci Shenzhen Inst Adv Technol Shenzhen Peoples R China Cent China Normal Univ Sch Math & Stat Hubei Key Lab Math Sci Wuhan Hubei Peoples R China Tanta Univ Prod Engn & Mech Design Dept Fac Engn Tanta Egypt Huazhong Univ Sci & Technol State Key Lab Digital Mfg Equipment & Technol Wuhan Hubei Peoples R China Misr Higher Inst Commerce & Comp Dept Comp Sci Mansoura Egypt Kafrelsheikh Univ Dept Mech Engn Fac Engn Kafrelsheikh Egypt Menoufia Univ Dept Math Fac Sci Shibin Al Kawm Egypt

This paper aims to solve an inverse heat conduction problem in two-dimensional space under transient regime, which consists of the estimation of multiple time-dependent heat sources placed at the boundaries. Robin boundary condition (third type boundary condition) is considered at the working domain boundary. The simultaneous identification problem is formulated as a constrained minimization problem using the output least squares method with Tikhonov regularization. The properties of the continuous and discrete optimization problem are studied. Differentiability results and the adjoint problems are established. The numerical estimation is investigated using a modified conjugate gradient method. Furthermore, to verify the performance of the proposed algorithm, obtained results are compared with results obtained from the well-known finite-element software COMSOL Multiphysics under the same conditions. The numerical results show that the proposed algorithm is accurate, robust and capable of simultaneously representing the time effects on reconstructing the time-dependent Robin coefficient and heat flux.

关键词： Inverse heat conduction problem numerical reconstruction modified conjugate gradient method Tikhonov's regularization

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A Gait Optimization Smoothing Penalty Function method for Bipedal Robot via DMOC

A Gait Optimization Smoothing Penalty Function Method for Bi...

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17th IFAC Symposium on System Identification (SYSID 2015)

作者： Sun, Zhongbo Li, Hongyang Wang, Jing Tian, Yantao Jilin Univ Minist Educ Coll Commun Engn Changchun 130023 Peoples R China Jilin Univ Minist Educ Key Lab Bion Engn Changchun 130023 Peoples R China

For periodic gait optimization problem of bipedal walking robot, based on discrete mechanics and optimal control (DMOC), a class of smoothing penalty function method is proposed. The optimal control strategy and trajectory are solved by a new smoothing exact penalty function algorithm. The algorithm Can quickly converge to a stable gait cycle independent, the selection of the initial gait, otherwise, the algorithm only needs one step correction and then generate a stable gait cycle. Numerical simulation results Show that the algorithm is feasible and effective. The algorithm makes the bipedal robot walk efficiently and stably on the even terrain. (C) 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Bipedal robot Smoothing penalty function method Discrete mechanics and optimal control Unconstrained optimization problem modified conjugate gradient method

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