Relevant bibliographies by topics / Hybrid conjugate gradient method

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Academic literature on the topic 'Hybrid conjugate gradient method'

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Published: 4 June 2021
Last updated: 19 June 2025

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Journal articles on the topic "Hybrid conjugate gradient method"

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Nur, Syarafina Mohamed, Mamat Mustafa, Rivaie Mohd, and Milleana Shaharudin Shazlyn. "A new hyhbrid coefficient of conjugate gradient method." Indonesian Journal of Electrical Engineering and Computer Science (IJEECS) 18, no. 3 (2020): 1454–63. https://doi.org/10.11591/ijeecs.v18.i3.pp1454-1463.

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Hybridization is one of the popular approaches in modifying the conjugate gradient method. In this paper, a new hybrid conjugate gradient is suggested and analyzed in which the parameter k is evaluated as a convex combination of RMIL k while using exact line search. The proposed method is shown to possess both sufficient descent and global convergence properties. Numerical performances show that the proposed method is promising and has overpowered other hybrid conjugate gradient methods in its number of iterations and central processing unit per time.
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Hafaidia, I., H. Guebbai, M. Al-Baali, and M. Ghiat. "A new hybrid conjugate gradient algorithm for unconstrained optimization." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 33, no. 2 (2023): 348–64. http://dx.doi.org/10.35634/vm230211.

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It is well known that conjugate gradient methods are useful for solving large-scale unconstrained nonlinear optimization problems. In this paper, we consider combining the best features of two conjugate gradient methods. In particular, we give a new conjugate gradient method, based on the hybridization of the useful DY (Dai-Yuan), and HZ (Hager-Zhang) methods. The hybrid parameters are chosen such that the proposed method satisfies the conjugacy and sufficient descent conditions. It is shown that the new method maintains the global convergence property of the above two methods. The numerical results are described for a set of standard test problems. It is shown that the performance of the proposed method is better than that of the DY and HZ methods in most cases.
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Liu, Jinkui. "A hybrid nonlinear conjugate gradient method." Lobachevskii Journal of Mathematics 33, no. 3 (2012): 195–99. http://dx.doi.org/10.1134/s1995080212030092.

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Hadji, Ghania, Yamina Laskri, Tahar Bechouat, and Rachid Benzine. "New Hybrid Conjugate Gradient Method as a Convex Combination of PRP and RMIL+ Methods." Studia Universitatis Babes-Bolyai Matematica 69, no. 2 (2024): 457–68. http://dx.doi.org/10.24193/subbmath.2024.2.14.

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The Conjugate Gradient (CG) method is a powerful iterative approach for solving large-scale minimization problems, characterized by its simplicity, low computation cost and good convergence. In this paper, a new hybrid conjugate gradient HLB method (HLB: Hadji-Laskri-Bechouat) is proposed and analysed for unconstrained optimization. By comparing numerically CGHLB with PRP and RMIL+ and by using the Dolan and More CPU performance, we deduce that CGHLB is more efficient. Keywords: Unconstrained optimization, hybrid conjugate gradient method, line search, descent property, global convergence.
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Ding, Lei, Yong Jun Luo, Yang Yang Wang, Zheng Li, and Bing Yin Yao. "Improved Method of Hybrid Genetic Algorithm." Applied Mechanics and Materials 556-562 (May 2014): 4014–17. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.4014.

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On account of low convergence of the traditional genetic algorithm in the late,a hybrid genetic algorithm based on conjugate gradient method and genetic algorithm is proposed.This hybrid algorithm takes advantage of Conjugate Gradient’s certainty, but also the use of genetic algorithms in order to avoid falling into local optimum, so it can quickly converge to the exact global optimal solution. Using Two test functions for testing, shows that performance of this hybrid genetic algorithm is better than single conjugate gradient method and genetic algorithm and have achieved good results.
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Fang, Minglei, Min Wang, Min Sun, and Rong Chen. "A Modified Hybrid Conjugate Gradient Method for Unconstrained Optimization." Journal of Mathematics 2021 (February 22, 2021): 1–9. http://dx.doi.org/10.1155/2021/5597863.

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The nonlinear conjugate gradient algorithms are a very effective way in solving large-scale unconstrained optimization problems. Based on some famous previous conjugate gradient methods, a modified hybrid conjugate gradient method was proposed. The proposed method can generate decent directions at every iteration independent of any line search. Under the Wolfe line search, the proposed method possesses global convergence. Numerical results show that the modified method is efficient and robust.
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Djordjevic, Snezana. "New hybrid conjugate gradient method as a convex combination of FR and PRP methods." Filomat 30, no. 11 (2016): 3083–100. http://dx.doi.org/10.2298/fil1611083d.

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We consider a newhybrid conjugate gradient algorithm,which is obtained fromthe algorithmof Fletcher-Reeves, and the algorithmof Polak-Ribi?re-Polyak. Numerical comparisons show that the present hybrid conjugate gradient algorithm often behaves better than some known algorithms.
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Yang, Xiangfei, Zhijun Luo, and Xiaoyu Dai. "A Global Convergence of LS-CD Hybrid Conjugate Gradient Method." Advances in Numerical Analysis 2013 (October 22, 2013): 1–5. http://dx.doi.org/10.1155/2013/517452.

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Conjugate gradient method is one of the most effective algorithms for solving unconstrained optimization problem. In this paper, a modified conjugate gradient method is presented and analyzed which is a hybridization of known LS and CD conjugate gradient algorithms. Under some mild conditions, the Wolfe-type line search can guarantee the global convergence of the LS-CD method. The numerical results show that the algorithm is efficient.
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Yao, Shengwei, and Bin Qin. "A Hybrid of DL and WYL Nonlinear Conjugate Gradient Methods." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/279891.

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The conjugate gradient method is an efficient method for solving large-scale nonlinear optimization problems. In this paper, we propose a nonlinear conjugate gradient method which can be considered as a hybrid of DL and WYL conjugate gradient methods. The given method possesses the sufficient descent condition under the Wolfe-Powell line search and is globally convergent for general functions. Our numerical results show that the proposed method is very robust and efficient for the test problems.
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Wang, Linjun, Liu Xu, Youxiang Xie, Yixian Du, and Xiao Han. "A new hybrid conjugate gradient method for dynamic force reconstruction." Advances in Mechanical Engineering 11, no. 1 (2019): 168781401882236. http://dx.doi.org/10.1177/1687814018822360.

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A new hybrid conjugate gradient method is proposed in this article based on the gradient operator and applied to the structural dynamic load identification problem. It has proved that the present method with the strong Wolfe line search possesses sufficient descent property. In addition, the present method is globally convergent when the parameter in the strong Wolfe line search conditions is restricted in some suitable intervals. Three example problems from engineering are solved by the newly developed conjugate gradient method to demonstrate the robustness and effectiveness of conjugate gradient method in solving multi-source dynamic load identification problems. Compared with the traditional Landweber iteration regularization method (Landweber), the proposed conjugate gradient method can more stably and effectively overcome the influences of noise, largely reduce the number of iterations, and provide accurate results in identifying multi-source dynamic force in practical engineering structure.
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Dissertations / Theses on the topic "Hybrid conjugate gradient method"

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Touati-Ahmed, Djamal. "A study of hybrid conjugate gradient methods." Thesis, Loughborough University, 1989. https://dspace.lboro.ac.uk/2134/13698.

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The main subject of the research in this thesis is the study of conjugate gradient methods for optimization and the development of improved algorithms. After an introductory first chapter, Chapter 2 contains a background of numerical methods for optimization in general and of conjugate gradient-type algorithms in particular. In Chapter 3 we study the convergence properties of conjugate gradient methods and discuss Powell's (1983) counter example that proves that there exist twice continuously differentiable functions with bounded level sets for which the Polak-Ribiere method fails to achieve global convergence whereas the Fletcher-Reeves method is shown to be globally convergent, despite the fact that in numerical computations the Polak-Ribiere method is far more efficient than that of Fletcher-Reeves. Chapters 4 and 5 deal with the development of a number of new hybrid algorithms, three of which are shown to satisfy the descent property at every iteration and achieve global convergence regardless of whether exact or inexact line searches are used. A new restarting procedure for conjugate gradient methods is also given that ensures a descent property to hold and global convergence for any conjugate gradient method using a non negative update. The application of these hybrid algorithms and that of the new restarting procedure to a wide class of well-known test problems is given and discussed in the final Chapter "Discussions and Conclusions". The results obtained, given in the appendices, show that a considerable improvement is achieved by these hybrids and by methods using the new restarting procedure over the existing conjugate gradient methods and also over quasi-Newton methods.
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Mohammadi, Seyed A. "A numerical study of some hybrid conjugate gradient methods in optimal control." Thesis, Loughborough University, 1995. https://dspace.lboro.ac.uk/2134/27361.

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The main work of this thesis is concerned with the comparison of conjugate gradient with hybrid conjugate gradient methods when they are applied to optimal control problems. Descriptions of the conjugate gradient. and hybrid conjugate gradient methods, for general optimisation, in finite and infinite dimensions are also given. The numerical methods for solving the differential equations and the line searches required in the optimisation are discussed next.
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Snežana, Đorđević. "Izbor parametara kod gradijentnih metoda za probleme optimizacije bez ograničenja." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2015. https://www.cris.uns.ac.rs/record.jsf?recordId=94106&source=NDLTD&language=en.

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Posmatra se problem optimizacije bez ograničenja. Za re&scaron;avanjeproblema&nbsp; optimizacije bez ograničenja postoji mno&scaron;tvo raznovrsnihmetoda. Istraživanje ovde motivisano je potrebom za metodama kojeće brzo konvergirati.Cilj je sistematizacija poznatih rezultata, kao i teorijska i numeričkaanaliza mogućnosti uvođenja parametra u gradijentne metode.Najpre se razmatra problem minimizacije konveksne funkcije vi&scaron;epromenljivih.Problem minimizacije konveksne funkcije vi&scaron;e promenljivih ovde sere&scaron;ava bez izračunavanja matrice hesijana, &scaron;to je naročito aktuelno zasisteme velikih dimenzija, kao i za probleme optimizacije kod kojihne raspolažemo ni tačnom vredno&scaron;ću funkcije cilja, ni tačnomvredno&scaron;ću gradijenta. Deo motivacije za istraživanjem ovde leži i upostojanju problema kod kojih je funkcija cilja rezultat simulacija.Numerički rezultati, predstavljeni u Glavi 6, pokazuju da uvođenjeizvesnog parametra može biti korisno, odnosno, dovodi do ubrzanjaodređenog metoda optimizacije.Takođe se predstavlja jedan novi hibridni metod konjugovanoggradijenta, kod koga je parametar konjugovanog gradijentakonveksna kombinacija dva poznata parametra konjugovanoggradijenta.U prvoj glavi opisuje se motivacija kao i osnovni pojmovi potrebni zapraćenje preostalih glava.U drugoj glavi daje se pregled nekih gradijentnih metoda prvog idrugog reda.Četvrta glava sadrži pregled osnovnih pojmova i nekih rezultatavezanih za metode konjugovanih gradijenata.Pomenute glave su tu radi pregleda nekih poznatih rezultata, dok seoriginalni doprinos predstavlja u trećoj, petoj i &scaron;estoj glavi.U trećoj glavi se opisuje izvesna modifikacija određenog metoda ukome se koristi multiplikativni parametar, izabran na slučajan način.Dokazuje se linearna konvergencija tako formiranog novog metoda.Peta glava sadrži originalne rezultate koji se odnose na metodekonjugovanih gradijenata. Naime, u ovoj glavi predstavlja se novihibridni metod konjugovanih gradijenata, koji je konveksnakombinacija dva poznata metoda konjugovanih gradijenata.U &scaron;estoj glavi se daju rezultati numeričkih eksperimenata, izvr&scaron;enihna&nbsp; izvesnom skupu test funkcija, koji se odnose na metode iz treće ipete glave. Implementacija svih razmatranih algoritama rađena je upaketu MATHEMATICA. Kriterijum upoređivanja je vreme radacentralne procesorske jedinice.6<br>The problem under consideration is an unconstrained optimizationproblem. There are many different methods made in aim to solve theoptimization problems.&nbsp; The investigation made here is motivated bythe fact that the methods which converge fast are necessary.The main goal is the systematization of some known results and alsotheoretical and numerical analysis of the possibilities to int roducesome parameters within gradient methods.Firstly, the minimization problem is considered, where the objectivefunction is a convex, multivar iable function. This problem is solvedhere without the calculation of Hessian, and such solution is veryimportant, for example, when the&nbsp; big dimension systems are solved,and also for solving optimization problems with unknown values ofthe objective function and its gradient. Partially, this investigation ismotivated by the existence of problems where the objective functionis the result of simulations.Numerical results, presented in&nbsp; Chapter&nbsp; 6, show that the introductionof a parameter is useful, i.e., such introduction results by theacceleration of the known optimization method.Further, one new hybrid conjugate gradient method is presented, inwhich the conjugate gradient parameter is a convex combination oftwo known conjugate gradient parameters.In the first chapter, there is motivation and also the basic co nceptswhich are necessary for the other chapters.The second chapter contains the survey of some first order andsecond order gradient methods.The fourth chapter contains the survey of some basic concepts andresults corresponding to conjugate gradient methods.The first, the second and the fourth&nbsp; chapters are here to help inconsidering of some known results, and the original results arepresented in the chapters 3,5 and 6.In the third chapter, a modification of one unco nstrained optimizationmethod is presented, in which the randomly chosen multiplicativeparameter is used. Also, the linear convergence of such modificationis proved.The fifth chapter contains the original results, corresponding toconjugate gradient methods. Namely, one new hybrid conjugategradient method is presented, and this&nbsp; method is the convexcombination of two known conjugate gradient methods.The sixth chapter consists of the numerical results, performed on a setof test functions, corresponding to methods in the chapters 3 and 5.Implementation of all considered algorithms is made in Mathematica.The comparison criterion is CPU time.<br>The problem under consideration is an unconstrained optimizationproblem. There are many different methods made in aim to solve theoptimization problems.&nbsp; The investigation made here is motivated bythe fact that the methods which converge fast are necessary.The main goal is the systematization of some known results and alsotheoretical and numerical analysis of the possibilities to int roducesome parameters within gradient methods.Firstly, the minimization problem is considered, where the objectivefunction is a convex, multivar iable function. This problem is solvedhere without the calculation of Hessian, and such solution is veryimportant, for example, when the&nbsp; big dimension systems are solved,and also for solving optimization problems with unknown values ofthe objective function and its gradient. Partially, this investigation ismotivated by the existence of problems where the objective functionis the result of simulations.Numerical results, presented in&nbsp; Chapter&nbsp; 6, show that the introductionof a parameter is useful, i.e., such introduction results by theacceleration of the known optimization method.Further, one new hybrid conjugate gradient method is presented, inwhich the conjugate gradient parameter is a convex combination oftwo known conjugate gradient parameters.In the first chapter, there is motivation and also the basic co nceptswhich are necessary for the other chapters.Key&nbsp; Words Documentation&nbsp; 97The second chapter contains the survey of some first order andsecond order gradient methods.The fourth chapter contains the survey of some basic concepts andresults corresponding to conjugate gradient methods.The first, the second and the fourth&nbsp; chapters are here to help inconsidering of some known results, and the original results arepresented in the chapters 3,5 and 6.In the third chapter, a modification of one unco nstrained optimizationmethod is presented, in which the randomly chosen multiplicativeparameter is used. Also, the linear convergence of such modificationis proved.The fifth chapter contains the original results, corresponding toconjugate gradient methods. Namely, one new hybrid conjugategradient method is presented, and this&nbsp; method is the convexcombination of two known conjugate gradient methods.The sixth chapter consists of the numerical results, performed on a setof test functions, corresponding to methods in the chapters 3 and 5.Implementation of all considered algorithms is made in Mathematica.The comparison criterion is CPU time
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Kopp, A. M., and D. L. Orlovskyi. "Business process model optimization using the conjugate gradient method." Thesis, Одеська національна академія харчових технологій, 2019. http://repository.kpi.kharkov.ua/handle/KhPI-Press/47102.

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This paper describes a model and a procedure of business process model optimization using the nonlinear conjugate gradient method. The research is based on business process modeling rules for BPMN (Business Process Model and Notation) as the de-facto standard for business process diagrams. Essential errors of business process modeling are outlined, as well as the metric used to define these shortcomings is denoted. Obtained results of business process model optimization are demonstrated.
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Michaud-Rioux, Vincent. "Real space DFT by locally optimal block preconditioned conjugate gradient method." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=110628.

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In condensed matter physics, atomistic first principle calculations are often necessary to achieve a microscopic understanding of the observed experimental phenomena and to make quantitative predictions of physical properties. In practice, atomic scale systems have irregularities (e.g. surface roughness) or defects (e.g. substitutional atoms or vacancies) that are too strong to be ignored or treated as small perturbations. In this thesis, we report the development of a real space DFT code for studying atomic scale systems from first principles. Our code, named MatRcal, which stands for "Matlab-based real space calculator", is developed in the technical computing language Matlab. The physics is described by density functional theory. The method itself is based on projecting the Kohn-Sham Hamiltonian on a uniform Cartesian grid. High-order finite-differencing is used to discretize the Laplacian operator. The potential due to the atomic nuclei is approximated with ab initio pseudopotentials. The pseudopotentials are generated following the procedure proposed by Troullier and Martins. We use the fully separable form introduced by Kleinman and Bylander. We argue that the method is simpler and yet has many advantages compared with conventional spectral methods. We provide relevant mathematical techniques and implementation details. In particular, we present and compare different eigensolvers used to diagonalize the Kohn-Sham Hamiltonian. We validate our software by comparing the HOMO-LUMO gaps of many organic and inorganic molecules obtained using our method with those obtained with the commercial code Gaussian. Our results are in excellent agreement. Our method gains in computational speed and algorithm parallelism, and its power in handling real space boundary conditions will be a major advantage for future applications in nanoelectronic device modelling.<br>En physique de la matière condensée, les calculs numériques sont souvent nécessaires pour parvenir à comprendre les phénomènes microscopiques observés lors d'expériences ou à prédire quantitativement des propriétés physiques. En pratique, les systèmes d'échelle atomique sont irréguliers (rugosité de surface) ou comportent des défauts (atomes de substitution ou lacunes), ce qui induit des effets trop sévères pour être ignorés ou traités comme des perturbations. Dans cette thèse, nous présentons une méthode qui permet d'étudier des systèmes d'échelle atomique à partir des lois fondamentales de la physique. Notre logiciel, nommé MatRcal, qui signifie "Matlab-based real space calculator", est développé dans le langage Matlab. La physique est décrite par la théorie de la fonctionnelle de la densité. La méthode projette l'Hamiltonien de Kohn-Sham sur un maillage Cartésien uniforme. Le calcul des différences finies est utilisé pour discrétiser l'opérateur Laplacien. Le potentiel dû aux noyaux atomiques est approximé par des pseudopotentiels non-empiriques. Les pseudopotentiels sont générés en suivant la procédure proposée par Troullier et Martins. Nous utilisons la forme séparable introduite par Kleinman et Bylander. Nous soutenons que la méthode est plus simple et pourtant présente de nombreux avantages par rapport aux conventionnelles méthodes spectrales. Nous introduisons plusieurs techniques mathématiques pertinentes à notre étude et certains détails d'implémentation. Entre autres, nous présentons et comparons plusieurs algorithmes de calcul de vecteurs propres utilisés pour diagonaliser l'Hamiltonien de Kohn-Sham. Nous validons notre méthode en comparant la largeur de bande interdite "HOMO-LUMO" de nombreuses molécules organiques et inorganiques prédites par notre méthode avec celles prédites par le logiciel commercial Gaussian. Notre méthode permet des gains en rapidité et en parallélisme, mais la possibilité de traiter des conditions limites non-périodiques sera le principal atout pour de futures simulations de dispositifs nanoélectroniques.
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Pester, M., and S. Rjasanow. "A parallel version of the preconditioned conjugate gradient method for boundary element equations." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800455.

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The parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two-dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large systems.
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MOSQUEIRA, DANIEL HUAMAN. "THE HYBRID BOUNDARY ELEMENT METHOD FOR GRADIENT ELASTICITY PROBLEMS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2013. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=23938@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO<br>Atualmente está bem difundido o uso de novas modelagens matemáticas para o estudo do comportamento de micro e nano sistemas mecânicos e eléctricos. O problema de escala é notável quando o tamanho das moléculas, partículas, grãos ou cristais de um sólido é relativamente considerável em relação ao comprimento do microdispositivo. Nesses casos a teoria clássica dos meios contínuos não descreve apropriadamente a solicitação estrutural e é necessária uma abordagem mais geral através de teorias generalizadas não-clássicas que contém a elasticidade clássica como um caso particular delas, onde os parâmetros constitutivos que representam às partículas são desprezíveis. Quando os efeitos microestruturais são importantes, o comportamento não responde como um material homogêneo se não como um material homogêneo. Cem anos atrás os irmãos Cosserat desenvolveram uma teoria de grãos rígidos imersos dentro de um macromeio elástico; posteriormente Toupin, Mindlin e outros pesquisadores na década de 60 formularam a chamada teoria gradiente de deformações, que recentemente é um objeto de muitas investigações analíticas e experimentais. Na década de oitenta, Aifantis e colaboradores conseguiram desenvolver uma teoria de gradiente de deformações simplificada, baseada em só uma constante elástica adicional não-clássica representativa da energia de deformação volumétrica para caracterizar satisfatoriamente os padrões dos fenômenos não-clássicos. Beskos e colaboradores estenderam o campo de aplicações da proposta inicial de Aifantis e fizeram as primeira implementações de elementos de contorno 2D e 3D para análises de elasticidade gradiente estática, no domínio da frequência e a mecânica da fratura. Desde o tempo de Toupin e Mindlin, procura-se estabelecer uma base variacional da teoria e uma formulação consistente das condições de contorno cinemáticas e de equilíbrio, o que parece ter tido êxito com os recentes trabalhos de Amanatidou e Aravas. Esta tese apresenta a formulação do método híbrido de elementos de contorno e finitos na elasticidade gradiente desenvolvida por Dumont e Huamán decompondo o potencial de Hellinger-Reissner em dois princípios de trabalhos virtuais: o primeiro em deslocamentos virtuais e o segundo em forças virtuais. Com esta finalidade é considerado além dos parâmetros clássicos, o trabalho realizado pelas tensões, deformações, forças e deslocamentos não-clássicos. É apresentado o desenvoltimento das soluções fundamentais singulares e polinomiais atráves das equações diferenciais de sexta ordem obtidas da equação de equilíbrio em termos de deslocamento na elasticidade gradiente. É apresentada também a aplicaçõ do método híbrido de contorno para problemas de tensão axial unidimensional e flexão bidimensional de vigas. Finalmente mostra-se a aplicação numérica do método em elementos finitos, é verificado o patch test de elementos finitos de diferentes ordem e mostra-se também análises de convergência.<br>The use of new mathematical modeling in the study of micro and Nano electro mechanical systems is currently becoming widespread. The scaling problem is apparent when the length of molecules, particles or grains immersed in the material is relatively important compared with the whole micro device dimension. Under this approach the classical theories of mechanics cannot describe suitably the structural requirement and it is necessary a more general outlook through non classical generalized theories which enclose the classical elasticity as a particular case where the non-classical constitutive parameters are negligible. When the microstructural effects are important, the material does not respond as a homogeneous but as a non-homogeneous one. A hundred years ago Cosserat brothers formulated a new theory of rigid grains which were embedded in an elastic macro medium; later Toupin, Mindlin along others researchers in 1960s developed a gradient strain theory which has been recently the source of many analystics and experimental investigations. In 1980s Ainfantis et al could develop a simplified strain gradient theory with just one additional non classical elastic constant which represents the volumetric elastic strain energy and characterized successfully the whole non classical pattern phenomenon. Beskos et al extended the treatment proposed initially by Aifantis and developed the first numerical applications for 2D and 3D boundary element methods and solved static as dynamic and crack problems. Since the times of Toupin and Mindlin it is looking for to establish a variational theory with a consistent cinematic and equilibrium boundary conditions, which seemed to have had success in the recent works of Amanatiodou and Aravas. This work presents the formulation of the hybrid boundary and finite element methods under the strain gradient scope which were developed by Dumont and Huamán through the versatile decomposition of the Hellinger-Reissner potential in two work principles: the displacements virtual work and the forces virtual work; both principles contain the virtual work performed by the non-classical magnitudes. Following, it is presented the complete development of singular and polynominal fundamental solutions abtained through the sixth order strain gradient differential equilibrium equations in terms of displacements. Next it is shown an application of the method to unidimensional truss element and bidimensional beam. Finally, it is presented a numerical application to strain gradient finite element, it is checked the patch tests to different elements orders and it is also shown a series of convergence analysis.
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BUENO, ANDRE LUIS CAVALCANTI. "SOLVING LARGE SYSTEMS OF LINEAR EQUATIONS ON MULTI-GPU CLUSTERS USING THE CONJUGATE GRADIENT METHOD IN OPENCLTM." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2013. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=22099@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>Sistemas de equações lineares esparsos e de grande porte aparecem como resultado da modelagem de vários problemas nas engenharias. Dada sua importância, muitos trabalhos estudam métodos para a resolução desses sistemas. Esta dissertação explora o potencial computacional de múltiplas GPUs, utilizando a tecnologia OpenCL, com a finalidade de resolver sistemas de equações lineares de grande porte. Na metodologia proposta, o método do gradiente conjugado é subdivido em kernels que são resolvidos por múltiplas GPUs. Para tal, se fez necessário compreender como a arquitetura das GPUs se relaciona com a tecnologia OpenCL a fim de obter um melhor desempenho.<br>The process of modeling problems in the engineering fields tends to produce substantiously large systems of sparse linear equations. Extensive research has been done to devise methods to solve these systems. This thesis explores the computational potential of multiple GPUs, through the use of the OpenCL tecnology, aiming to tackle the solution of large systems of sparse linear equations. In the proposed methodology, the conjugate gradient method is subdivided into kernels, which are delegated to multiple GPUs. In order to achieve an efficient method, it was necessary to understand how the GPUs’ architecture communicates with OpenCL.
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Habbestad, Torstein. "An FPGA-based implementation of the Conjugate Gradient Method used to solve Large Dense Systems of Linear Equations." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for elektronikk og telekommunikasjon, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-15403.

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To find the solution to large dense systems have always been a very time consuming problem, this thesis tries to accelerate this problem by implementing an highly pipelined conjugate gradient method on an FPGA, it has been used to solve dense systems of linear equations and has been tested and compared to a software version of the algorithm. The FPGA where capable of utilizing 90 % of the available memory bandwidth, in addition it is shown that the FPGA implemented Conjugate Gradient Method can be 30x faster compared to a custom made Conjugate Gradient method in software.
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Barajas, Leandro G. "Process Control in High-Noise Environments Using A Limited Number Of Measurements." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/7741.

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The topic of this dissertation is the derivation, development, and evaluation of novel hybrid algorithms for process control that use a limited number of measurements and that are suitable to operate in the presence of large amounts of process noise. As an initial step, affine and neural network statistical process models are developed in order to simulate the steady-state system behavior. Such models are vitally important in the evaluation, testing, and improvement of all other process controllers referred to in this work. Afterwards, fuzzy logic controller rules are assimilated into a mathematical characterization of a model that includes the modes and mode transition rules that define a hybrid hierarchical process control. The main processing entity in such framework is a closed-loop control algorithm that performs global and then local optimizations in order to asymptotically reach minimum bias error; this is done while requiring a minimum number of iterations in order to promptly reach a desired operational window. The results of this research are applied to surface mount technology manufacturing-lines yield optimization. This work achieves a practical degree of control over the solder-paste volume deposition in the Stencil Printing Process (SPP). Results show that it is possible to change the operating point of the process by modifying certain machine parameters and even compensate for the difference in height due to change in print direction.
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Books on the topic "Hybrid conjugate gradient method"

1

S, Liou M., and Lewis Research Center. Institute for Computational Mechanics in Propulsion., eds. On the application of chimera/unstructured hybrid grids for conjugate heat transfer. NASA Lewis Research Center, ICOMP, 1995.

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Meng-Sing, Liou, and Lewis Research Center. Institute for Computational Mechanics in Propulsion., eds. On the application of chimera/unstructured hybrid grids for conjugate heat transfer. NASA Lewis Research Center, ICOMP, 1995.

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Pan, Victor. A fast, preconditioned conjugate gradient Toeplitz solver. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1989.

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Chronopoulos, Anthony. A class of parallel iterative methods implemented on multiprocessors. University of Illinois at Urbana-Champaign, Dept. of Computer Science, 1986.

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Lustman, Liviu. A three dimensional calculation of elastic equilibrium for composite materials. ICASE, 1986.

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Center, Langley Research, ed. Multi-color incomplete Cholesky conjugate gradient methods for vector computers. National Aeronautics and Space Administration, Langley Research Center, 1986.

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Shaw, Scott. Comparison of the convergence behaviour of three linear solvers for large, sparse unsymmetric matrices. Dept. of Aerospace Science, College of Aeronautics, Cranfield University, 1995.

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Arthur, Raefsky, Hager Bradford H, and Jet Propulsion Laboratory (U.S.), eds. Finite elements and the method of conjugate gradients on a concurrent processor. National Aeronautics and Space Administration, Jet Propulsion Laboratory, California Institute of Technology?, 1985.

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Branch, Mary Ann. A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems. Cornell Theory Center, Cornell University, 1995.

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1956-, Volakis John Leonidas, and Ames Research Center, eds. Applications of the conjugate gradient FFT method in scattering and radiation including simulations with impedance boundary conditions. Radiation Laboratory, Dept. of Electrical Engineering and Computer Science, University of Michigan, 1991.

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Book chapters on the topic "Hybrid conjugate gradient method"

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Andrei, Neculai. "Hybrid and Parameterized Conjugate Gradient Methods." In Nonlinear Conjugate Gradient Methods for Unconstrained Optimization. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-42950-8_6.

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Mohamed, Nur Syarafina, Mohd Rivaie, Norhaslinda Zullpakkal, and Shazlyn Milleana Shaharuddin. "Performance of a New Hybrid Conjugate Gradient Method." In SpringerBriefs in Applied Sciences and Technology. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-55558-9_5.

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Alkhouli, Talat, Hatem S. A. Hamatta, Mustafa Mamat, and Mohd Rivaie. "An Efficient Hybrid Conjugate Gradient Method for Unconstrained Optimisation." In Forum for Interdisciplinary Mathematics. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-8498-5_9.

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Azamuddin, Ain Aqiela, Nurul ‘Aini, Mohd Rivaie, and Zuraida Alwadood. "New Hybrid Conjugate Gradient Method Under Exact Line Search." In Proceedings of the International Conference on Mathematical Sciences and Statistics 2022 (ICMSS 2022). Atlantis Press International BV, 2022. http://dx.doi.org/10.2991/978-94-6463-014-5_10.

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Oladepo, David A., Olawale J. Adeleke, and Churchill T. Ako. "A Mixed Hybrid Conjugate Gradient Method for Unconstrained Engineering Optimization Problems." In Advances in Intelligent Systems and Computing. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91192-2_42.

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Alker, Manfred, Sönke Frantz, Karl Rohr, and H. Siegfried Stiehl. "Hybrid Optimization for 3D Landmark Extraction:Genetic Algorithms and Conjugate Gradient Method." In Bildverarbeitung für die Medizin 2002. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-55983-9_73.

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Zhang, Jiapu. "The Hybrid Method of Steepest Descent: Conjugate Gradient with Simulated Annealing." In Molecular Structures and Structural Dynamics of Prion Proteins and Prions. Springer Netherlands, 2015. http://dx.doi.org/10.1007/978-94-017-7318-8_11.

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Wakatani, Akiyoshi. "Hybrid Parallel Approach of Splitting-Up Conjugate Gradient Method for Distributed Memory Multicomputers." In Lecture Notes in Networks and Systems. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-12385-7_82.

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Adeleke, Olawale J., Micheal O. Olusanya, and Idowu A. Osinuga. "A PRP-HS Type Hybrid Nonlinear Conjugate Gradient Method for Solving Unconstrained Optimization Problems." In Intelligent Systems Applications in Software Engineering. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30329-7_6.

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Bartels, Sören. "Conjugate Gradient Method." In UNITEXT. Springer Berlin Heidelberg, 2025. https://doi.org/10.1007/978-3-662-70890-3_16.

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Conference papers on the topic "Hybrid conjugate gradient method"

1

Hanan Wan Osman, Wan Farah. "A Globally Convergent Improved Hybrid Method of Quasi Newton and Conjugate Gradient Method." In 2024 11th International Conference on Electrical Engineering, Computer Science and Informatics (EECSI). IEEE, 2024. https://doi.org/10.1109/eecsi63442.2024.10776393.

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Shorinwa, Ola, and Mac Schwager. "Distributed Conjugate Gradient Method via Conjugate Direction Tracking." In 2024 American Control Conference (ACC). IEEE, 2024. http://dx.doi.org/10.23919/acc60939.2024.10644588.

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Yu, Wenyi, and Chao Zhang. "An Optimizer for Conformer Based on Conjugate Gradient Method." In 2024 IEEE 14th International Symposium on Chinese Spoken Language Processing (ISCSLP). IEEE, 2024. https://doi.org/10.1109/iscslp63861.2024.10800306.

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Hassan, Basim A., and Ahmed S. Ahmed. "Effect Conjugate Gradient Method for Solving Nonlinear Optimization Problems." In 2024 8th International Symposium on Multidisciplinary Studies and Innovative Technologies (ISMSIT). IEEE, 2024. https://doi.org/10.1109/ismsit63511.2024.10757267.

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Yang, Shuangye, Benyu Wang, Liangbo Hu, et al. "A conjugate gradient method for solving unconstrained optimization problems." In 2024 6th International Conference on Intelligent Control, Measurement and Signal Processing (ICMSP). IEEE, 2024. https://doi.org/10.1109/icmsp64464.2024.10867051.

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Hassan, Basim A., Hisham M. Khudhur, and Ayman W. Jasim. "New Version Conjugate Gradient Method for Image Impulse Noise Removals." In 2024 8th International Symposium on Multidisciplinary Studies and Innovative Technologies (ISMSIT). IEEE, 2024. https://doi.org/10.1109/ismsit63511.2024.10757200.

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Dong, Junli, and Baocong Jiao. "A New Hybrid PRP-DY Conjugate Gradient Method." In 2010 Third International Joint Conference on Computational Science and Optimization. IEEE, 2010. http://dx.doi.org/10.1109/cso.2010.27.

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Dong, Junli, Baocong Jiao, and Lanping Chen. "A New Hybrid HS-DY Conjugate Gradient Method." In 2011 Fourth International Joint Conference on Computational Sciences and Optimization (CSO). IEEE, 2011. http://dx.doi.org/10.1109/cso.2011.47.

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Zhou, Guangming, and Yunzhi Gan. "Hybrid conjugate gradient method for solving fuzzy nonlinear equations." In 2010 International Conference on Logistics Systems and Intelligent Management (ICLSIM). IEEE, 2010. http://dx.doi.org/10.1109/iclsim.2010.5461380.

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Ahmed, Myasar A., and Maha S. Younis. "A new hybrid conjugate gradient method for unconstraint optimization." In 1ST SAMARRA INTERNATIONAL CONFERENCE FOR PURE AND APPLIED SCIENCES (SICPS2021): SICPS2021. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0121648.

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Reports on the topic "Hybrid conjugate gradient method"

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Peters, Timothy J. Application of a Conjugate Gradient Method to the Synthesis of Phase-Only Planar Arrays. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada233756.

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Biffle, J. H. JAC3D -- A three-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method; Yucca Mountain Site Characterization Project. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/138710.

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Biffle, J. H., and M. L. Blanford. JAC2D: A two-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method; Yucca Mountain Site Characterization Project. Office of Scientific and Technical Information (OSTI), 1994. http://dx.doi.org/10.2172/145293.

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Computer program for solving ground-water flow equations by the preconditioned conjugate gradient method. US Geological Survey, 1987. http://dx.doi.org/10.3133/wri874091.

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