Relevant bibliographies by topics / Newton algorithms

Academic literature on the topic 'Newton algorithms'

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Published: 6 September 2023

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Journal articles on the topic "Newton algorithms"

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Lu, Pei Xin. "Research on BP Neural Network Algorithm Based on Quasi-Newton Method." Applied Mechanics and Materials 686 (October 2014): 388–94. http://dx.doi.org/10.4028/www.scientific.net/amm.686.388.

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With more and more researches about improving BP algorithm, there are more improvement methods. The paper researches two improvement algorithms based on quasi-Newton method, DFP algorithm and L-BFGS algorithm. After fully analyzing the features of quasi-Newton methods, the paper improves BP neural network algorithm. And the adjustment is made for the problems in the improvement process. The paper makes empirical analysis and proves the effectiveness of BP neural network algorithm based on quasi-Newton method. The improved algorithms are compared with the traditional BP algorithm, which indicates that the improved BP algorithm is better.
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KISETA, Jacques SABITI, and Roger LIENDI AKUMOSO. "A Review of Well-Known Robust Line Search and Trust Region Numerical Optimization Algorithms for Solving Nonlinear Least-Squares Problems." International Science Review 2, no. 3 (November 9, 2021): 1–17. http://dx.doi.org/10.47285/isr.v2i3.106.

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The conditional, unconditional, or the exact maximum likelihood estimation and the least-squares estimation involve minimizing either the conditional or the unconditional residual sum of squares. The maximum likelihood estimation (MLE) approach and the nonlinear least squares (NLS) procedure involve an iterative search technique for obtaining global rather than local optimal estimates. Several authors have presented brief overviews of algorithms for solving NLS problems. Snezana S. Djordjevic (2019) presented a review of some unconstrained optimization methods based on the line search techniques. Mahaboob et al. (2017) proposed a different approach to estimate nonlinear regression models using numerical methods also based on the line search techniques. Mohammad, Waziri, and Santos (2019) have briefly reviewed methods for solving NLS problems, paying special attention to the structured quasi-Newton methods which are the family of the search line techniques. Ya-Xiang Yuan (2011) reviewed some recent results on numerical methods for nonlinear equations and NLS problems based on online searches and trust regions techniques, particularly on Levenberg-Marquardt type methods, quasi-Newton type methods, and trust regions algorithms. The purpose of this paper is to review some online searches and trust region's more well-known robust numerical optimization algorithms and the most used in practice for the estimation of time series models and other nonlinear regression models. The line searches algorithms considered are: Gradient algorithm, Steepest Descent (SD) algorithm, Newton-Raphson (NR) algorithm, Murray’s algorithm, Quasi-Newton (QN) algorithm, Gauss-Newton (GN) algorithm, Fletcher and Powell algorithm (FP), Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. While the only trust-region algorithm considered is the Levenberg-Marquardt (LM) algorithm. We also give some main advantages and disadvantages of these different algorithms.
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Xu, Xiang-Rong, Won-Jee Chung, Young-Hyu Choi, and Xiang-Feng Ma. "A new dynamic formulation for robot manipulators containing closed kinematic chains." Robotica 17, no. 3 (May 1999): 261–67. http://dx.doi.org/10.1017/s0263574799001320.

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This paper presents a new recursive algorithm of robot dynamics based on the Kane's dynamic equations and Newton-Euler formulations. Differing from Kane's work, the algorithm is general-purpose and can be easily realized on computers. It is suited not only for robots with all rotary joints but also for robots with some prismatic joints. Formulations of the algorithm keep the recurrence characteristics of the Newton-Euler formulations, but possess stronger physical significance. Unlike the conventional algorithms, such as the Lagrange and Newton-Euler algorithm, etc., the algorithm can be used to deal with dynamics of robots containing closed chains without cutting the closed chains open. In addition, this paper makes a comparison between the algorithm and those conventional algorithms from the number of multiplications and additions.
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Dussault, Jean-Pierre. "High-order Newton-penalty algorithms." Journal of Computational and Applied Mathematics 182, no. 1 (October 2005): 117–33. http://dx.doi.org/10.1016/j.cam.2004.11.043.

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Cai, Xiao-Chuan, and David E. Keyes. "Nonlinearly Preconditioned Inexact Newton Algorithms." SIAM Journal on Scientific Computing 24, no. 1 (January 2002): 183–200. http://dx.doi.org/10.1137/s106482750037620x.

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Gościniak, Ireneusz, and Krzysztof Gdawiec. "Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and Modifications." Entropy 22, no. 7 (July 2, 2020): 734. http://dx.doi.org/10.3390/e22070734.

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There is a huge group of algorithms described in the literature that iteratively find solutions of a given equation. Most of them require tuning. The article presents root-finding algorithms that are based on the Newton–Raphson method which iteratively finds the solutions, and require tuning. The modification of the algorithm implements the best position of particle similarly to the particle swarm optimisation algorithms. The proposed approach allows visualising the impact of the algorithm’s elements on the complex behaviour of the algorithm. Moreover, instead of the standard Picard iteration, various feedback iteration processes are used in this research. Presented examples and the conducted discussion on the algorithm’s operation allow to understand the influence of the proposed modifications on the algorithm’s behaviour. Understanding the impact of the proposed modification on the algorithm’s operation can be helpful in using it in other algorithms. The obtained images also have potential artistic applications.
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Taher, Mardeen Sh, and Salah G. Shareef. "A Combined Conjugate Gradient Quasi-Newton Method with Modification BFGS Formula." International Journal of Analysis and Applications 21 (April 3, 2023): 31. http://dx.doi.org/10.28924/2291-8639-21-2023-31.

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The conjugate gradient and Quasi-Newton methods have advantages and drawbacks, as although quasi-Newton algorithm has more rapid convergence than conjugate gradient, they require more storage compared to conjugate gradient algorithms. In 1976, Buckley designed a method that combines the CG method with QN updates, which is better than that observed for conjugate gradient algorithms but not as good as the quasi-Newton approach. This type of method is called the preconditioned conjugate gradient (PCG) method. In this paper, we introduce two new preconditioned conjugate gradient (PCG) methods that combine conjugate gradient with a new update of quasi-Newton methods. The new quasi-Newton method satisfied the positive define, and the direction of the new preconditioned conjugate gradient is descent direction. In numerical results, it is showing the new preconditioned conjugate gradient method is more effective on several high-dimension test problems than standard preconditioning.
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Zhang, Liping. "A Newton-Type Algorithm for Solving Problems of Search Theory." Advances in Operations Research 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/513918.

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In the survey of the continuous nonlinear resource allocation problem, Patriksson pointed out that Newton-type algorithms have not been proposed for solving the problem of search theory in the theoretical perspective. In this paper, we propose a Newton-type algorithm to solve the problem. We prove that the proposed algorithm has global and superlinear convergence. Some numerical results indicate that the proposed algorithm is promising.
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Bo, Liefeng, Ling Wang, and Licheng Jiao. "Recursive Finite Newton Algorithm for Support Vector Regression in the Primal." Neural Computation 19, no. 4 (April 2007): 1082–96. http://dx.doi.org/10.1162/neco.2007.19.4.1082.

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Some algorithms in the primal have been recently proposed for training support vector machines. This letter follows those studies and develops a recursive finite Newton algorithm (IHLF-SVR-RFN) for training nonlinear support vector regression. The insensitive Huber loss function and the computation of the Newton step are discussed in detail. Comparisons with LIBSVM 2.82 show that the proposed algorithm gives promising results.
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Aghamiry, H. S., A. Gholami, and S. Operto. "Full waveform inversion by proximal Newton method using adaptive regularization." Geophysical Journal International 224, no. 1 (September 11, 2020): 169–80. http://dx.doi.org/10.1093/gji/ggaa434.

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SUMMARY Regularization is necessary for solving non-linear ill-posed inverse problems arising in different fields of geosciences. The base of a suitable regularization is the prior expressed by the regularizer, which can be non-adaptive or adaptive (data-driven), smooth or non-smooth, variational-based or not. Nevertheless, tailoring a suitable and easy-to-implement prior for describing geophysical models is a non-trivial task. In this paper, we propose two generic optimization algorithms to implement arbitrary regularization in non-linear inverse problems such as full-waveform inversion (FWI), where the regularization task is recast as a denoising problem. We assess these optimization algorithms with the plug-and-play block matching (BM3D) regularization algorithm, which determines empirical priors adaptively without any optimization formulation. The non-linear inverse problem is solved with a proximal Newton method, which generalizes the traditional Newton step in such a way to involve the gradients/subgradients of a (possibly non-differentiable) regularization function through operator splitting and proximal mappings. Furthermore, it requires to account for the Hessian matrix in the regularized least-squares optimization problem. We propose two different splitting algorithms for this task. In the first, we compute the Newton search direction with an iterative method based upon the first-order generalized iterative shrinkage-thresholding algorithm (ISTA), and hence Newton-ISTA (NISTA). The iterations require only Hessian-vector products to compute the gradient step of the quadratic approximation of the non-linear objective function. The second relies on the alternating direction method of multipliers (ADMM), and hence Newton-ADMM (NADMM), where the least-squares optimization subproblem and the regularization subproblem in the composite objective function are decoupled through auxiliary variable and solved in an alternating mode. The least-squares subproblem can be solved with exact, inexact, or quasi-Newton methods. We compare NISTA and NADMM numerically by solving FWI with BM3D regularization. The tests show promising results obtained by both algorithms. However, NADMM shows a faster convergence rate than NISTA when using L-BFGS to solve the Newton system.
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Dissertations / Theses on the topic "Newton algorithms"

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Wei, Ermin. "Distributed Newton-type algorithms for network resource allocation." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/60822.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 99-101).
Most of today's communication networks are large-scale and comprise of agents with local information and heterogeneous preferences, making centralized control and coordination impractical. This motivated much interest in developing and studying distributed algorithms for network resource allocation problems, such as Internet routing, data collection and processing in sensor networks, and cross-layer communication network design. Existing works on network resource allocation problems rely on using dual decomposition and first-order (gradient or subgradient) methods, which involve simple computations and can be implemented in a distributed manner, yet suffer from slow rate of convergence. Second-order methods are faster, but their direct implementation requires computation intensive matrix inversion operations, which couple information across the network, hence cannot be implemented in a decentralized way. This thesis develops and analyzes Newton-type (second-order) distributed methods for network resource allocation problems. In particular, we focus on two general formulations: Network Utility Maximization (NUM), and network flow cost minimization problems. For NUM problems, we develop a distributed Newton-type fast converging algorithm using the properties of self-concordant utility functions. Our algorithm utilizes novel matrix splitting techniques, which enable both primal and dual Newton steps to be computed using iterative schemes in a decentralized manner with limited information exchange. Moreover, the step-size used in our method can be obtained via an iterative consensus-based averaging scheme. We show that even when the Newton direction and the step-size in our method are computed within some error (due to finite truncation of the iterative schemes), the resulting objective function value still converges superlinearly to an explicitly characterized error neighborhood. Simulation results demonstrate significant convergence rate improvement of our algorithm relative to the existing subgradient methods based on dual decomposition. The second part of the thesis presents a distributed approach based on a Newtontype method for solving network flow cost minimization problems. The key component of our method is to represent the dual Newton direction as the limit of an iterative procedure involving the graph Laplacian, which can be implemented based only on local information. Using standard Lipschitz conditions, we provide analysis for the convergence properties of our algorithm and show that the method converges superlinearly to an explicitly characterized error neighborhood, even when the iterative schemes used for computing the Newton direction and the stepsize are truncated. We also present some simulation results to illustrate the significant performance gains of this method over the subgradient methods currently used.
by Ermin Wei.
S.M.
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Saadallah, A. F. "A new approach to quasi-Newton methods for minimization." Thesis, University of Essex, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.380374.

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Klemes, Marek Carleton University Dissertation Engineering Electronics. "Fast robust Quasi-Newton adaptive algorithms for general array processing." Ottawa, 1996.

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Ghandhari, R. A. "On the use of function values to improve quasi-Newton methods." Thesis, University of Essex, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328658.

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Harrison, Anthony Westbrook. "Algorithms for Computing the Lattice Size." Kent State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=kent1529781033957183.

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Sassi, Carlos Alberto. "Sobre o desempenho de métodos Quase-Newton e aplicações." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306041.

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Orientador: Maria Aparecida Diniz Ehrhardt
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-16T22:41:08Z (GMT). No. of bitstreams: 1 Sassi_Carlos_M.pdf: 2431422 bytes, checksum: 7e2d7456777a9a43cc62a5524d3fca93 (MD5) Previous issue date: 2010
Resumo: Iniciamos este trabalho com o estudo de equações não lineares, transcendentais de uma única variável, com o objetivo principal de abordar sistemas de equações não lineares, analisar os métodos, algoritmos e realizar testes computacionais, embasados na plataforma MatLab "The Language of Technical computer - R2008a - version 7.6.0.324_. Os algoritmos tratados se referem ao método de Newton, métodos Quase-Newton, método Secante e aplicações, com enfoque na H-equação de Chandrasekhar. Estudamos aspectos de convergência de cada um destes métodos que puderam ser analisados na prática, a partir dos experimentos numéricos realizados
Abstract: This work begins with the study of nonlinear and transcendental equations, with only one variable, which has the main purpose to study systems of nonlinear equations, methods and algoritms, in order to accomplish computational tests using MatLab Codes "The Language of Technical computer - R2008a - version 7.6.0.324". These algoritms were concerned to Newton's method, Quasi-Newton method, Secant method, and the main application was the Chandrasekhar H-Equation. Convergence studies for these methods were analysed with the applied numerical methods
Mestrado
Matematica
Mestre em Matemática
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Gaujoux, Renaud Gilles. "Resolução de sistema KKT por metodo de tipo Newton não diferenciavel." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306442.

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Orientador: Roberto Andreani
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-04T05:03:19Z (GMT). No. of bitstreams: 1 Gaujoux_RenaudGilles_M.pdf: 1743739 bytes, checksum: a3548a59bc983f4398cb0136c62c1d6a (MD5) Previous issue date: 2005
Resumo: Esta dissertação trata da aplicação de um método de tipo Newton generalizado aos sistemas KKT. Graças às funções chamadas de NCP, o sistema KKT pode ser reformulado como uma equação do tipo H(z) = O, onde H é uma função semi-suave. Nos preliminares teóricos apresentamos os conceitos importantes para a análise desse tipo de sistema quando a função involvida não é diferenciável. Trata-se de subdiferencial, semi-suavidade, semi-derivada. Então, usando um ponto de vista global, descrevemos de uma vez só as diferentes generalizações do método de Newton, apresentando as condições suficientes de convergência local. Uma versão globalizada do método é também detalhada. Com o fim de aplicar o algoritmo à reformulação semi-suave do sistema KKT, estudamos as propriedades da função H, primeiro independentemente da função NCP usada. Então analisamos o caso de três funções NCP particulares: a função do Mínimo, a função de Fischer-Burmeister, a função de Fischer-Burmeister Penalizada. Apresentamos os resultados de testes numéricos que comparam o desempenho do algoritmo quando usa as diferentes funções NCP acima
Abstract: This work deals with the use of generalized Newton type method to solve KKT systems. By the mean of so called NCP functions, any KKT system can be writen as an equation of type H(z) = O, where H is a semismooth function. In a teorical preliminaries part, we present some key notions for the analysis of such a type of system, whose the involved function is not differentiable. It deals with subdifferential, semismoothness, semiderivative. Then, tackling the problem with a very general point of view, we make a unified description of different generalizations of N ewton method, giving sufficient local convergence conditions. More over, we detail a possible globalization of such methods. In order to use this global algorithm to solve semismooth form of KKT systems, we study some of the H function's properties, first without specifying any underlying NCP function, and then in the case of three known NCP functions: the minimum function, the Fischer-Burmeister function and the penalized Fischer-Burmeister function. Finally, we give the results of numerical tests, which compare the algorithm's performance for each of these three NCP functions
Mestrado
Matematica Aplicada
Mestre em Matemática Aplicada
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Woodgate, K. G. "Optimization over positive semi-definite symmetric matrices with application to Quasi-Newton algorithms." Thesis, Imperial College London, 1987. http://hdl.handle.net/10044/1/46914.

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Zanjácomo, Paulo Régis. "On weighted paths for nonlinear semidefinite complementarity problems and newton methods for semidefinite programming." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/21680.

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Hüeber, Stefan. "Discretization techniques and efficient algorithms for contact problems." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-36087.

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Books on the topic "Newton algorithms"

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Kuan, Chung-Ming. A recurrent Newton algorithm and its convergence properties. Champaign: University of Illinois at Urbana-Champaign, 1993.

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Deuflhard, P. Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2011.

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D, Gropp W., and Langley Research Center, eds. Globalized Newton-Krylov-Schwarz algorithms and software for parallel implicit CFD. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1998.

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1962-, Cai Xiao-Chuan, Institute for Computer Applications in Science and Engineering., and Langley Research Center, eds. Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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D, Gropp W., and Langley Research Center, eds. Globalized Newton-Krylov-Schwarz algorithms and software for parallel implicit CFD. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1998.

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1962-, Cai Xiao-Chuan, and Langley Research Center, eds. Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation: NASA contract no. NAS1-19480. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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1962-, Cai Xiao-Chuan, and Langley Research Center, eds. Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation: NASA contract no. NAS1-19480. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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1962-, Cai Xiao-Chuan, and Langley Research Center, eds. Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation: NASA contract no. NAS1-19480. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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Paul, Casasent David, Hall Ernest L, and Society of Photo-optical Instrumentation Engineers., eds. Intelligent robots and computer vision XX: Algorithms, techniques, and active vision : 29-31 October, 2001, Newton [Massachusetts] USA. Bellingham, Wash., USA: SPIE, 2001.

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Kostyukov, Viktor. Molecular mechanics of biopolymers. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1010677.

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The monograph is devoted to molecular mechanics simulations of biologically important polymers like proteins and nucleic acids. It is shown that the algorithms based on the classical laws of motion of Newton, with high-quality parameterization and sufficient computing resources is able to correctly reproduce and predict the structure and dynamics of macromolecules in aqueous solution. Summarized the development path of biopolymers molecular mechanics, its theoretical basis, current status and prospects for further progress. It may be useful to researchers specializing in molecular Biophysics and molecular biology, as well as students of senior courses of higher educational institutions, studying the biophysical and related areas of training.
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Book chapters on the topic "Newton algorithms"

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Sima, Vasile. "Newton Algorithms." In Algorithms for Linear-Quadratic Optimization, 97–196. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003067450-2.

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Bhatnagar, S., H. Prasad, and L. Prashanth. "Newton-Based Smoothed Functional Algorithms." In Stochastic Recursive Algorithms for Optimization, 133–48. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-4285-0_8.

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Bhatnagar, S., H. Prasad, and L. Prashanth. "Newton-Based Simultaneous Perturbation Stochastic Approximation." In Stochastic Recursive Algorithms for Optimization, 105–31. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-4285-0_7.

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Schröter, M., and O. Sauer. "Quasi-Newton Algorithms for Medical Image Registration." In IFMBE Proceedings, 433–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03882-2_115.

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Pedersen, C., and P. Thoft-Christensen. "Interactive Structural Optimization with Quasi-Newton Algorithms." In Reliability and Optimization of Structural Systems, 225–32. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-0-387-34866-7_23.

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Sommars, Jeff, and Jan Verschelde. "Pruning Algorithms for Pretropisms of Newton Polytopes." In Computer Algebra in Scientific Computing, 489–503. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45641-6_31.

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Kanzow, Christian. "An Active Set-Type Newton Method for Constrained Nonlinear Systems." In Complementarity: Applications, Algorithms and Extensions, 179–200. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4757-3279-5_9.

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Evtushenko, Yu G., and V. G. Zhadan. "Stable Barrier-Projection and Barrier-Newton Methods for Linear and Nonlinear Programming." In Algorithms for Continuous Optimization, 255–85. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-009-0369-2_9.

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Poloni, Federico. "Newton method for rank-structured algebraic Riccati equations." In Algorithms for Quadratic Matrix and Vector Equations, 131–43. Pisa: Scuola Normale Superiore, 2011. http://dx.doi.org/10.1007/978-88-7642-384-0_8.

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Christensen, Peter W., and Jong-Shi Pang. "Frictional Contact Algorithms Based on Semismooth Newton Methods." In Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, 81–116. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-6388-1_5.

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Conference papers on the topic "Newton algorithms"

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Tsinos, Christos G., and Paulo S. R. Diniz. "Data-selective LMS-Newton and LMS-Quasi-Newton Algorithms." In ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2019. http://dx.doi.org/10.1109/icassp.2019.8683076.

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Pillutla, Krishna, Vincent Roulet, Sham M. Kakade, and Zaid Harchaoui. "Modified Gauss-Newton Algorithms under Noise." In 2023 IEEE Statistical Signal Processing Workshop (SSP). IEEE, 2023. http://dx.doi.org/10.1109/ssp53291.2023.10207977.

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Koshevoy, Gleb, and Denis Mironov. "F-polynomials & Newton polytopes." In 2022 24th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2022. http://dx.doi.org/10.1109/synasc57785.2022.00017.

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Bhotto, Md Zulfiquar Ali, and Andreas Antoniou. "Improved data-selective LMS-Newton adaptation algorithms." In 2009 16th International Conference on Digital Signal Processing (DSP). IEEE, 2009. http://dx.doi.org/10.1109/icdsp.2009.5201148.

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Singh, V. K., and K. C. Gupta. "A Manipulator Jacobian Based Modified Newton-Raphson Algorithm (JMNR) for Robot Inverse Kinematics." In ASME 1989 Design Technical Conferences. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/detc1989-0142.

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Abstract This paper deals with the formulation of a manipulator Jacobian based Newton-Raphson algorithm for robot inverse kinematics. A strict descent feature has been incorporated into the algorithm to make it robust. Previous studies with Newton-Raphson type matrix iteration have produced an overdetermined system of linear equations which relates small changes in the joint variables. Dealing with these extra equations led to computational inefficiency. Previous manipulator Jacobian based predictor-corrector algorithms for inverse kinematics avoided this inefficiency, but these required either a variable time step or a small fixed time step; also special attention was required to start these algorithms. Motivated by the advantages of these two methods, this paper presents a robust manipulator Jacobian based Newton-Raphson algorithm for robot inverse kinematics.
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Masetti, Giulio, Silvano Chiaradonna, and Felicita di Giandomenico. "Exploring equations ordering influence on variants of the Newton-Raphson method." In NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS (NUMTA–2016): Proceedings of the 2nd International Conference “Numerical Computations: Theory and Algorithms”. Author(s), 2016. http://dx.doi.org/10.1063/1.4965417.

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Foltyn, Ladislav, and Oldřich Vlach. "Implementation of full linearization in semismooth Newton method for 2D contact problem." In Programs and Algorithms of Numerical Mathematics 18. Institute of Mathematics, Czech Academy of Sciences, 2017. http://dx.doi.org/10.21136/panm.2016.04.

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Nikpour, M., J. H. Manton, and R. Mahony. "Novel Newton algorithms for the Hermitian eigenvalue problem." In Information, Decision and Control. IEEE, 2002. http://dx.doi.org/10.1109/idc.2002.995439.

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Wills, Adrian G., and Thomas B. Schon. "On the construction of probabilistic Newton-type algorithms." In 2017 IEEE 56th Annual Conference on Decision and Control (CDC). IEEE, 2017. http://dx.doi.org/10.1109/cdc.2017.8264638.

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Tiexiang Li, Eric King-wah Chu, and Xuan Zhao. "Robust pole assignment via the Schur-Newton algorithms." In 2011 International Conference on Multimedia Technology (ICMT). IEEE, 2011. http://dx.doi.org/10.1109/icmt.2011.6002622.

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Reports on the topic "Newton algorithms"

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Saleh, R. A., J. K. White, A. R. Newton, and A. L. Sangiovanni-Vincentelli. Accelerating Relaxation Algorithms for Circuit Simulation Using Waveform-Newton and Step-Size Refinement. Fort Belvoir, VA: Defense Technical Information Center, October 1988. http://dx.doi.org/10.21236/ada200774.

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Joseph, Ilon. Code Coupling via Jacobian-Free Newton-Krylov Algorithms with Application to Magnetized Fluid Plasma and Kinetic Neutral Models. Office of Scientific and Technical Information (OSTI), May 2014. http://dx.doi.org/10.2172/1249135.

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McHugh, P. R. An investigation of Newton-Krylov algorithms for solving incompressible and low Mach number compressible fluid flow and heat transfer problems using finite volume discretization. Office of Scientific and Technical Information (OSTI), October 1995. http://dx.doi.org/10.2172/130602.

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Arhin, Stephen, Babin Manandhar, Hamdiat Baba Adam, and Adam Gatiba. Predicting Bus Travel Times in Washington, DC Using Artificial Neural Networks (ANNs). Mineta Transportation Institute, April 2021. http://dx.doi.org/10.31979/mti.2021.1943.

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Washington, DC is ranked second among cities in terms of highest public transit commuters in the United States, with approximately 9% of the working population using the Washington Metropolitan Area Transit Authority (WMATA) Metrobuses to commute. Deducing accurate travel times of these metrobuses is an important task for transit authorities to provide reliable service to its patrons. This study, using Artificial Neural Networks (ANN), developed prediction models for transit buses to assist decision-makers to improve service quality and patronage. For this study, we used six months of Automatic Vehicle Location (AVL) and Automatic Passenger Counting (APC) data for six Washington Metropolitan Area Transit Authority (WMATA) bus routes operating in Washington, DC. We developed regression models and Artificial Neural Network (ANN) models for predicting travel times of buses for different peak periods (AM, Mid-Day and PM). Our analysis included variables such as number of served bus stops, length of route between bus stops, average number of passengers in the bus, average dwell time of buses, and number of intersections between bus stops. We obtained ANN models for travel times by using approximation technique incorporating two separate algorithms: Quasi-Newton and Levenberg-Marquardt. The training strategy for neural network models involved feed forward and errorback processes that minimized the generated errors. We also evaluated the models with a Comparison of the Normalized Squared Errors (NSE). From the results, we observed that the travel times of buses and the dwell times at bus stops generally increased over time of the day. We gathered travel time equations for buses for the AM, Mid-Day and PM Peaks. The lowest NSE for the AM, Mid-Day and PM Peak periods corresponded to training processes using Quasi-Newton algorithm, which had 3, 2 and 5 perceptron layers, respectively. These prediction models could be adapted by transit agencies to provide the patrons with accurate travel time information at bus stops or online.
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Canonico, Rosangela, and Luca Parisi. The Newman Janis Algorithm: A Review of Some Results. GIQ, 2012. http://dx.doi.org/10.7546/giq-12-2011-159-169.

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Canonico, Rosangela, and Luca Parisi. Theoretical Models For Astrophysical Objects and the Newman-Janis Algorithm. GIQ, 2012. http://dx.doi.org/10.7546/giq-11-2010-85-96.

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Allen, Luke, Joon Lim, Robert Haehnel, and Ian Detwiller. Rotor blade design framework for airfoil shape optimization with performance considerations. Engineer Research and Development Center (U.S.), June 2021. http://dx.doi.org/10.21079/11681/41037.

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A framework for optimizing rotor blade airfoil shape is presented. The framework uses two digital workflows created within the Galaxy Simulation Builder (GSB) software package. The first is a workflow enabling the automated creation of a surrogate model for predicting airfoil performance coefficients. An accurate surrogate model for the rapid generation of airfoil coefficient tables has been developed using linear interpolation techniques that is based on C81Gen and ARC2D CFD codes. The second workflow defines the rotor blade optimization problem using GSB and the Dakota numerical optimization library. The presented example uses a quasi-Newton optimization algorithm to optimize the tip region of the UH-60A main rotor blade with respect to vehicle performance. This is accomplished by morphing the blade tip airfoil shape for optimum power, subject to a constraint on the maximum pitch link load.
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