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An optimization derivation of the method of conjugate gradients [PDF]
, 2020 We give a derivation of the method of conjugate gradients based on the requirement that each iterate minimizes a strictly convex quadratic on the space spanned by the previously observed gradients. Rather than verifying that the search direction has the correct properties, we show that generation of such iterates is equivalent to generation of ...
Ek, David, Forsgren, Anders
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Spectral CG Algorithm for Solving Fuzzy Non-linear Equations
Iraqi Journal for Computer Science and Mathematics, 2022 The non-linear conjugate gradient method is a very effective technique for addressing Large-Scale minimization problems, and it has a wide range of applications in Mathematics, Chemistry, Physics, Engineering, and Medicine, etc.
Mezher M. Abed +2 more
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Tikrit Journal of Pure Science, 2023 In this paper a new three–term Conjugate Gradient (CG) method is suggested, the derivation of the method based on the descent property and conjugacy condition, the global convergence property is analyzed; numerical results indicate that the new proposed
Abbas Y. Al-Bayati +2 more
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On the solutions to Sylvester‐conjugate periodic matrix equations via iteration
IET Control Theory & Applications, 2023 The problem of solving a class of Sylvester‐conjugate periodic matrix equations is investigated in this paper. Utilising conjugate gradient method, an iterative algorithm is provided, from which a matrix sequence can be generated to approximate the ...
Lei Zhang +5 more
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A Method of Two New Augmented Lagrange Multiplier Versions for Solving Constrained Problems
International Journal of Mathematics and Mathematical Sciences, 2022 One of the more restrictive methods of improvement is the augmented Lagrange method. Two versions are built in the external framework and the internal framework of the proposed method.
Hamsa Th. Saeed Chilmeran +3 more
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Algorithms of through calculation for damage processes [PDF]
Компьютерные исследования и моделирование, 2018 The paper reviews the existing approaches to calculating the destruction of solids. The main attention is paid to algorithms using a unified approach to the calculation of deformation both for nondestructive and for the destroyed states of the material ...
Nikolay G. Burago, I. S. Nikitin
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Algorithms for calculation damage processes
Fracture and Structural Integrity, 2019 The paper reviews the existing approaches to calculating the destruction of solids. The main attention is paid to algorithms using a unified approach to the calculation of deformation both for nondestructive and for the destroyed states of the material ...
Nikolay G. Burago +3 more
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Application of Laplace Domain Waveform Inversion to Cross-Hole Radar Data
Remote Sensing, 2019 Full waveform inversion (FWI) can yield high resolution images and has been applied in Ground Penetrating Radar (GPR) for around 20 years. However, appropriate selection of the initial models is important in FWI because such an inversion is highly ...
Xu Meng, Sixin Liu, Yi Xu, Lei Fu
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Frontiers in Applied Mathematics and StatisticsThis study introduced an efficient method for solving non-linear equations. Our approach enhances the traditional spectral conjugate gradient parameter, resulting in significant improvements in the resolution of complex nonlinear problems. This innovative technique ensures global convergence and descent condition supported by carefully considered ...
Ghulam Abbass +5 more
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Engineering ReportsThis research introduces two conjugate gradient methods, BIV1 and BIV2, designed to enhance the efficiency and performance of unconstrained optimization problems with only first derivative vectors.
Bassim A. Hassan +3 more
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