Academic literature on the topic 'Newton-Raphson method'

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Journal articles on the topic "Newton-Raphson method"

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Torres-Hernandez, A., and F. Brambila-Paz. "Fractional Newton-Raphson Method." Applied Mathematics and Sciences An International Journal (MathSJ) 8, no. 1 (March 31, 2021): 1–13. http://dx.doi.org/10.5121/mathsj.2021.8101.

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The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n, with n ∈ N. However, this method is limited since it diverges for the case in which polynomials only have complex roots if a real initial condition is taken. In the present work, we explain an iterative method that is created using the fractional calculus, which we will call the Fractional Newton-Raphson (F N-R) Method, which has the ability to enter the space of complex numbers given a real initial condition, which allows us to find both the real and complex roots of a polynomial unlike the classical Newton-Raphson method.
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Verbeke, Johan, and Ronald Cools. "The Newton‐Raphson method." International Journal of Mathematical Education in Science and Technology 26, no. 2 (March 1995): 177–93. http://dx.doi.org/10.1080/0020739950260202.

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Mehtre, Vishal V. "Root Finding Methods: Newton Raphson Method." International Journal for Research in Applied Science and Engineering Technology 7, no. 11 (November 30, 2019): 411–14. http://dx.doi.org/10.22214/ijraset.2019.11065.

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Maxrizal, Maxrizal. "Modifikasi Garis Singgung Untuk Mempercepat Iterasi Pada Metode Newton Raphson." Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi 11, no. 2 (December 14, 2023): 351–60. http://dx.doi.org/10.37905/euler.v11i2.23094.

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The Newton-Raphson method is one of the methods to find solutions or roots of nonlinear equations. This method converges faster than other methods and is more effective in finding doubles. In this study, it will be shown that the Newton-Raphson modification uses modifications to the tangent equation. The results show that for every nth iteration, the speed difference of Newton Raphson modification is __. Furthermore, the convergence of Newton Raphson is __, and for Newton Raphson modification is __.
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RAMADHANI UTAMI, NANDA NINGTYAS, I. NYOMAN WIDANA, and NI MADE ASIH. "PERBANDINGAN SOLUSI SISTEM PERSAMAAN NONLINEAR MENGGUNAKAN METODE NEWTON-RAPHSON DAN METODE JACOBIAN." E-Jurnal Matematika 2, no. 2 (May 31, 2013): 11. http://dx.doi.org/10.24843/mtk.2013.v02.i02.p032.

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System of nonlinear equations is a collection of some nonlinear equations. The Newton-Raphson method and Jacobian method are methods used for solving systems of nonlinear equations. The Newton-Raphson methods uses first and second derivatives and indeed does perform better than the steepest descent method if the initial point is close to the minimizer. Jacobian method is a method of resolving equations through iteration process using simultaneous equations. If the Newton-Raphson methods and Jacobian methods are compared with the exact value, the Jacobian method is the closest to exact value but has more iterations. In this study the Newton-Raphson method gets the results faster than the Jacobian method (Newton-Raphson iteration method is 5 and 58 in the Jacobian iteration method). In this case, the Jacobian method gets results closer to the exact value.
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Mehtre, Vishal Vaman. "Review on Newton Raphson Method." International Journal for Research in Applied Science and Engineering Technology 7, no. 11 (November 30, 2019): 669–71. http://dx.doi.org/10.22214/ijraset.2019.11107.

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Ng, S. W., and Y. S. Lee. "Variable dimension Newton-Raphson method." IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 47, no. 6 (June 2000): 809–17. http://dx.doi.org/10.1109/81.852933.

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He, Ji-Huan. "A modified Newton-Raphson method." Communications in Numerical Methods in Engineering 20, no. 10 (June 10, 2004): 801–5. http://dx.doi.org/10.1002/cnm.664.

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Qureshi, Umair Khalid, Sanaullah Jamali, Zubair Ahmed Kalhoro, and Guan Jinrui. "Deprived of Second Derivative Iterated Method for Solving Nonlinear Equations." Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences 58, no. 2 (December 24, 2021): 39–44. http://dx.doi.org/10.53560/ppasa(58-2)605.

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Non-linear equations are one of the most important and useful problems, which arises in a varied collection of practical applications in engineering and applied sciences. For this purpose, in this paper has been developed an iterative method with deprived of second derivative for the solution of non-linear problems. The developed deprived of second derivative iterative method is convergent quadratically, and which is derived from Newton Raphson Method and Taylor series. The numerical results of the developed method are compared with the Newton Raphson Method and Modified Newton Raphson Method. From graphical representation and numerical results, it has been observed that the deprived of second derivative iterative method is more appropriate and suitable as accuracy and iteration perception by the valuation of Newton Raphson Method and Modified Newton Raphson Method for estimating a non-linear problem.
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Syafii, Mohamad, Rahmi Ridhallah, and Rizki Amalia Nur. "Penerapan Metode Newton Raphson untuk Pencarian Akar pada Fungsi Kompleks." JOSTECH Journal of Science and Technology 3, no. 1 (March 31, 2023): 71–78. http://dx.doi.org/10.15548/jostech.v3i1.5685.

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This study aims to compare analytical methods and numerical methods in determining the roots of equations of a complex function. The numerical method used in this research is the Newton Raphson method. In this study two examples of complex functions were given, after which the roots of the equation were searched using the analytical method and the Newton Raphson method, then the results were compared. In this study, two examples are given, namely and . In example one, three different roots were obtained analytically, while numerical calculations using the Newton Raphson method obtained a value that converged to one of the roots that had been obtained analytically. In example two, four different roots were obtained analytically, while numerically using the Newton Raphson method similarly if done using the Newton Raphson method, a value that converged to one of the roots that had been obtained analytically was obtained.
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Dissertations / Theses on the topic "Newton-Raphson method"

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Silva, Renato de Sousa e. "Raiz de função polinomial pelo método de Newton-Raphson." Universidade Federal de Goiás, 2018. http://repositorio.bc.ufg.br/tede/handle/tede/8735.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Determining roots of polynomial functions is a quite frequent content in the subject of Mathematics in Primary and Higher Education. But Galois has shown that it is not possible to develop algebraic formulas to find such roots in polynomials with a degree greater than 4. The present work aims to use Newton-Raphson’s Numerical and Iterative method to find roots of polynomial function. For this, the GeoGebra software is used as a computational and pedagogical tool to illustrate the procedure adopted by the mentioned method through spreadsheets, Geometry and algebraic calculations. Thus, the proposed methodology can help in the understanding of the Newton-Raphson Method and contribute to the process of teaching and learning the content of polynomials for teachers and students of Basic Education.
Determinar raízes de funções polinomiais é um conteúdo bastante frequente na disciplina de Matemática do Ensino Básico e Superior. Mas, Galois demonstrou que não é possível desenvolver fórmulas algébricas para encontrar tais raízes em polinômios com grau maior que 4. Então o presente trabalho tem o objetivo de utilizar o Método Numérico e Iterativo de Newton-Raphson para encontrar raízes de função polinomial. Para isto, utiliza-se o software GeoGebra como ferramenta computacional e pedagógica para ilustrar o procedimento adotado pelo método citado por meio de planilhas eletrônicas, da Geometria e de cálculos algébricos. Assim, a metodologia proposta pode auxiliar na compreensão do Método de Newton-Raphson e colaborar para o processo de ensino e aprendizagem do conteúdo de polinômios para professores e alunos do Ensino Básico.
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Miller, Shannon N. "The dynamics of Newton's method on cubic polynomials." Huntington, WV : [Marshall University Libraries], 2006. http://www.marshall.edu/etd/descript.asp?ref=658.

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Garcia-Valle, Rodrigo Joel. "Dynamic modelling and simulation of electric power systems using the Newton-Raphson method." Thesis, University of Glasgow, 2007. http://theses.gla.ac.uk/435/.

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The research work presented in this thesis is concerned with the development of a dynamic power flow computer algorithm using Newton's method. It addresses both the development of a positive sequence dynamic power flow algorithm for the dynamic study of balanced power systems and a fully-fledged three-phase dynamic power flow algorithm for the dynamic study of power systems exhibiting a significant degree of either structural or operational unbalance. As a prelude to the research work on dynamic power flows, a three-phase Newton-Raphson power flow algorithm in rectangular co-ordinates with conventional HVDC power plant modelling is presented in this thesis, emphasising the representation of converter control modes. The solution approach takes advantage of the strong numerical solutions for combined HVAC-HVDC systems, where power plant and operational imbalances are explicitly taken into account. The dynamic algorithm is particularly suited to carrying out long-term dynamic simulations and voltage stability assessments. Dynamic model representations of the power plants components and the load tap changing transformer are considered, and to widen the study range of dynamic voltage phenomena using this method, extensions have been made to include induction motor and polynomial load modelling features. Besides, reactive power compensators that base their modus operandi on the switching of power electronic valves, such as HVDC-VSC and the STATCOM are taken into account. The dynamic power flow algorithm has primarily been developed making use of the positive sequence and [dq] representations. Extensions are made to developing a three-phase power flows dynamic algorithm. Test cases for the various dynamic elements developed in this research are presented to show the versatility of the models and simulation tool, including a trip cascading event leading up to a wide-area voltage collaps. Comparisons with the output of a conventional transient stability program carried out where appropriate.
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Simonis, Joseph P. "Inexact Newton methods applied to under-determined systems." Link to electronic dissertation, 2006. http://www.wpi.edu/Pubs/ETD/Available/etd-050406-103442/.

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Dissertation (Ph.D.)--Worcester Polytechnic Institute.
Keywords: Periodic Solutions, Under-Determined Systems, Continuation, Nonlinear Eigenvalue, Inexact Newton Methods, Newton's Method, Trust Region Methods Includes bibliographical references (p.93-95).
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Choi, Yan-yu. "Residual Julia sets of Newton's maps and Smale's problems on the efficiency of Newton's method." Click to view the E-thesis via HKUTO, 2006. http://sunzi.lib.hku.hk/hkuto/record/B37680948.

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Choi, Yan-yu, and 蔡欣榆. "Residual Julia sets of Newton's maps and Smale's problems on the efficiency of Newton's method." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B37680948.

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Baur, Robin. "An Investigation of Rupture in Thin Fluid Films." Scholarship @ Claremont, 2005. https://scholarship.claremont.edu/hmc_theses/177.

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The behavior of a fluid with a thin capillary meniscus can be modelled on a one-dimensional domain Ω = [−L, L] by the thin film equation ht = −(hnhxxx)x with boundary conditions hx(±L) = ±α (giving a fixed contact angle) and hxxx(±L) = 0 (prohibiting mass flux). It is desirable to know whether or not such a film experiences rupture; that is, whether there exists some x0, t0 (with t0 possibly ∞) such that h(x0, t0) = 0, corresponding to the appearance of a dry spot. We approach this problem using energy methods, which use the conservation or dissipation of quantities such as mass, surface area, coating energy, and other more abstract quantities to describe the behavior of the fluid. We present a brief analysis of the behavior of some of these energies, as well as a proof that, given certain assumptions, rupture cannot occur in a thin capillary meniscus for n > 4 and, in more restricted cases, for n > 7/2. We also show that rupture must occur for 0 < n < 1/2. We describe the asymptotic behavior of the regions in which rupture occurs. We also describe the numerical implementation of this problem and the advantages and drawbacks of using certain prewritten solvers in MATLAB and new implementations of θ-weighted schemes and the Newton-Raphson method. We propose uses of these numerical methods to make further progress on the problem.
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Tran, Vanthu Thy. "Newton's method as a mean value method." Akron, OH : University of Akron, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=akron1176739678.

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Thesis (M.S.)--University of Akron, Dept. of Mathematics, 2007.
"May, 2007." Title from electronic thesis title page (viewed 4/28/2009) Advisor, Ali Hajjafar; Faculty readers, Linda Marie Saliga, Lala Krishna; Department Chair, Joseph W. Wilder; Dean of the College, Ronald F. Levant; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.
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Santos, Elma Pereira 1982. "Despacho integrado da geração termeletrica e da produção e transporte de gas natural com metodo de Newton." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/259919.

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Orientador: Takaaki Ohishi
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: O gás natural é um combustível fóssil que pode ser utilizado tanto na indústria como no comércio, residências e veículos. Uma aplicação importante do gás natural é como fonte primária para geração de energia elétrica em usinas termelétricas. Seu uso possibilita uma maior estabilidade ao Sistema Elétrico Brasileiro, pelo fato de depender menos do nível de água nos reservatórios para atendimento da demanda de energia elétrica. Como o gás natural possui uma estocagem complexa e onerosa, a quantidade de demanda de gás afeta diretamente as suas etapas de produção e transporte, já que toda a quantidade produzida e transportada deverá ser consumida. Desse modo, a operação do sistema de suprimento de gás natural é fortemente dependente das decisões de seus consumidores. As usinas termelétricas estão entre os maiores consumidores de gás, de forma que o despacho das usinas termelétricas afeta fortemente a operação do sistema de gás. Por outro lado, restrições no sistema de suprimento de gás também podem afetar a operação das usinas termelétricas. Esta forte dependência operativa entre estes dois sistemas requer uma operação coordenada para se obter uma operação mais eficiente e segura. Esta tese apresenta um modelo de despacho econômico aplicado a usinas termelétricas que usam gás natural como fonte primária, considerando os custos de produção, transporte de gás natural e de geração de energia elétrica. A modelagem matemática resulta em um problema misto não linear. Para resolução foi utilizada uma abordagem híbrida, que combina um modelo baseado em Programação Linear e um modelo não linear. O problema não linear é resolvido através do método de Newton.
Abstract: Natural gas is a fossil fuel that can be used in industry, trade, residence and vehicles, among others. An important application of natural gas is as a primary source for electricity generation in thermoelectric power plants. In the Brazilian Electric System this source increase the system stability, once it is less dependent of the water level in tanks to serve the demand for power. As natural gas storage it is more complex and expensive, the amount of gas directly affects the production and transportation stages, once the entire amount that is produced and transported must be consumed. Thus, the operation of the supply system of natural gas is strongly dependent on decisions of their consumers. The thermoelectric power plants are among the largest gas consumers, so the dispatch of thermoelectric plants affects strongly the gas system operation. On the other hand, restrictions in the gas supply system may also affect the operation of thermoelectric plants. This strong operative dependence between these two kinds of systems, requires a coordinated operation with the aim of obtaining a more efficient and safer operation. This thesis presents a model of economic dispatch applied to thermoelectric power plants that use natural gas as a primary energy source, considering the costs of production, transportation of the natural gas and electricity generation. The mathematical modeling results in a nonlinear mixed problem. For resolution was used a hybrid approach that combines a model based on Linear Programming and a nonlinear. The nonlinear problem is solved by the Newton's method.
Mestrado
Engenharia de Computação
Mestre em Engenharia Elétrica
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Meireles, Eduardo David. "Uma contribuição ao estudo do problema de mal condicionamento de redes eletricas de potencia sob o ponto de vista de estabilidade de tensão." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261719.

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Orientadores: Carlos Alberto de Castro Junior, Luiz Carlos Pereira da Silva
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: A literatura técnica registra uma série de metodologias propostas para a obtenção do estado de operação das chamadas redes mal condicionadas, ou seja, redes cujos modelos resultam em sistemas de equações de difícil resolução [1, 2]. Estas metodologias mostraram-se úteis também em situações em que a operação da rede é infactível, ou seja, situações em que o sistema de equações que representa a rede não apresenta soluções. Nestes casos, os métodos de resolução do problema de fluxo de carga convencionais divergem, não oferecendo informações úteis sobre a rede. Já as metodologias específicas para redes mal condicionadas oferecem, mesmo na situação de divergência, informações que podem ser úteis no sentido de apontar suas possíveis causas. Recentemente, foi levantada a possibilidade de que estas supostas redes mal condicionadas não existissem de fato, mas estivessem simplesmente operando em torno do seu limite de estabilidade de tensão [3], ou seja, o mal condicionamento seria resultado de problemas de estabilidade de tensão e não do mal condicionamento propriamente dito. De acordo com [3], após uma série de simulações não foram encontradas situações em que a rede fosse mal condicionada e estivesse operando em condições normais de operação no que diz respeito à estabilidade de tensão. Os testes mostrados em [3] foram realizados utilizando-se o fluxo de carga da continuação [4]. O objetivo deste trabalho é realizar alguns testes para analisar e discutir as conclusões de [3]. Para isso, algumas simulações adicionais foram realizadas para redes teste mal condicionadas apresentadas em [2], dentre outras. As conclusões deste trabalho apontam para a importância de se continuar a pesquisa para o desenvolvimento de métodos para a resolução de sistemas mal condicionados
Abstract: A number of methods for computing the operating state of the so-called ill-conditioned systems can be found in the literature. A power system is called ill-conditioned if its model results in a set of equations for which the resolution presents numerical difficulties [1, 2]. Those methods also showed to be useful tools in situations where the operation is unfeasible, that is, situations in which the set of equations that represents the network do not present any solution. In these cases the conventional load flow methods diverge and do not provide any useful information about the system operating condition. On the other hand, specific load flow methods for ill-conditioned systems do provide such information, even in divergence situations, and the possible causes of the numerical problems may be inferred. Recently, the possibility that the alleged ill-conditioned systems are in fact systems operating close to or beyond their voltage stability limit was discussed [3]. Therefore, the ill-conditioning would be the result of voltage stability problems rather than ill-conditioning itself. According to [3], after a number of simulations no situations where found such that the system was indeed ill-conditioned and was operating in normal condition as far as voltage stability is concerned. The tests carried out in [3] used continuation load method [4]. The main goal of this work is to carry out some simulation tests to analyze and discuss the conclusion presented in [3]. Also, some additional simulations were done for other ill-conditioned systems shown in [2], among others. The conclusions of this work point towards the importance of a continuing effort in the development of efficient methods for solving ill-conditioned systems
Mestrado
Energia Eletrica
Mestre em Engenharia Elétrica
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Books on the topic "Newton-Raphson method"

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Radzik, Tomasz. Newton's method for fractional combinatorial optimization. Stanford, Calif: Dept. of Computer Science, Stanford University, 1992.

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Scott, James R. A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations. [Washington, DC: National Aeronautics and Space Administration, 1993.

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Kelley, C. T. Solving nonlinear equations with Newton's method. Philadelphia: Society for Industrial and Applied Mathematics, 2003.

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Hohmann, Andreas. Inexact Gauss Newton methods for parameter dependent nonlinear problems. Aachen: Shaker, 1994.

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Kikō, Genshiryoku Anzen Kiban. Heisei 20-nendo uFLOW, INS kōdo no kairyō to shi-kaiseki. [Tokyo]: Genshiryoku Anzen Kiban Kikō, 2010.

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Parresol, Bernard R. Recovering parameters of Johnson's SB distribution. Asheville, NC: U.S. Dept. of Agriculture, Forest Service, Southern Research Station, 2003.

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Center, Langley Research, ed. Optimum suction distribution for transition control. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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Center, Langley Research, ed. Optimum suction distribution for transition control. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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Arian, Eyal. Approximation of the Newton step by a defect correction process. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1999.

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United States. National Aeronautics and Space Administration., ed. NPAC--nozzle performance analysis code. [Washington, DC: National Aeronautics and Space Administration, 1997.

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Book chapters on the topic "Newton-Raphson method"

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Dedieu, Jean-Pierre. "Newton-Raphson Method." In Encyclopedia of Applied and Computational Mathematics, 1023–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_374.

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Awange, Joseph L., Erik W. Grafarend, Béla Paláncz, and Piroska Zaletnyik. "Extended Newton-Raphson method." In Algebraic Geodesy and Geoinformatics, 101–10. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12124-1_8.

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Yamaguchi, Fujio. "Geometric Newton-Raphson Method." In Computer-Aided Geometric Design, 299–324. Tokyo: Springer Japan, 2002. http://dx.doi.org/10.1007/978-4-431-67881-6_15.

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Awange, Joseph L., and Béla Paláncz. "Extended Newton-Raphson Method." In Geospatial Algebraic Computations, 113–24. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-25465-4_8.

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Lootsma, Freerk A. "An Asynchronous Newton-Raphson Method." In Supercomputing, 367–76. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-75771-6_25.

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Hanief, Mohammad. "Combined Regula–Falsi and Newton–Raphson Method." In Advances in Mechanical Engineering, 123–32. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0942-8_11.

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Selig, J. M., and Hui Li. "A Geometric Newton-Raphson Method for Gough-Stewart Platforms." In Computational Kinematics, 183–90. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01947-0_23.

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Paul, Aakash, and Shyamalendu Kandar. "Generation of Pseudo Random Sequence Using Modified Newton Raphson Method." In Communications in Computer and Information Science, 250–62. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0404-1_18.

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Véstias, Mário P., and Horácio C. Neto. "Decimal Division Using the Newton–Raphson Method and Radix-1000 Arithmetic." In Embedded Systems Design with FPGAs, 31–54. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-1362-2_2.

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Bhowmick, Suman. "Introduction to the Newton—Raphson Method and the Power Flow Problem." In Flexible AC Transmission Systems (FACTS), 33–61. Boca Raton: Taylor & Francis, 2016.: CRC Press, 2018. http://dx.doi.org/10.1201/9781315222431-2.

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Conference papers on the topic "Newton-Raphson method"

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Rao, Dhage Navaneet, Ganne Sai Charan, Degala Veera Venkata Sairam, and Kamatchi S. "Posit Number Division using Newton-Raphson method." In 2021 International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT). IEEE, 2021. http://dx.doi.org/10.1109/icaect49130.2021.9392582.

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Sideri, Athina, and Efstathios Stiliaris. "A Newton-Raphson Accelerated Iterative Reconstruction Method." In 2020 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC). IEEE, 2020. http://dx.doi.org/10.1109/nss/mic42677.2020.9507867.

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Wenzhu, Sun, Cao Jianping, Fu Zhanping, and Deng Haifeng. "Head Posture Recognition Based on Newton-Raphson Method." In ICCPR 2020: 2020 9th International Conference on Computing and Pattern Recognition. New York, NY, USA: ACM, 2020. http://dx.doi.org/10.1145/3436369.3436370.

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Chen, Chang-New. "The Global Secant Relaxation-Based Accelerated Iteration Procedure for Solution of Nonlinear Finite Element Equation Systems of Offshore Structural Mechanics Problems." In ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2011. http://dx.doi.org/10.1115/omae2011-50170.

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A global secant relaxation (GSR)-based accelerated iteration scheme can be used to carry out the incremental/iterative solution of various nonlinear finite element systems of offshore structural mechanics problems. This computation procedure can overcome the possible deficiency of numerical instability caused by local failure existing in the iterative computation. Moreover, this method can efficiently accelerate the convergency of the iterative computation. This incremental/iterative analysis can consistently be carried out to update the response history up to a near ultimate load stage, which is important for investigating the global failure behaviour of a structure under certain external cause, if the constant stiffness is used. Consequently, this method can widely be used to solve general nonlinear problems. Mathematical procedures of Newton-Raphson techniques in finite element methods for nonlinear finite element problems are summarized. These techniques are the Newton-Raphson method, quasi-Newton methods, modified Newton-Raphson methods and accelerated modified Newton-Raphson methods. Numerical results obtained by using various accelerated modified Newton-Raphson methods are used to study the convergency performances of these techniques for material nonlinearity problems and deformation nonlinearity problems, separately.
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Sameni, Ali, Alexandre B. Nassif, Chandrabhanu Opathella, and Bala Venkatesh. "A modified Newton-Raphson method for unbalanced distribution systems." In 2012 IEEE International Conference on Smart Grid Engineering (SGE). IEEE, 2012. http://dx.doi.org/10.1109/sge.2012.6463955.

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Jmii, Hajer, Asma Meddeb, and Souad Chebbi. "Newton-Raphson Load Flow Method for Voltage Contingency Ranking." In 2018 15th International Multi-Conference on Systems, Signals & Devices (SSD). IEEE, 2018. http://dx.doi.org/10.1109/ssd.2018.8570626.

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Zhang, Wanjun, Feng Zhang, Jingxuan Zhang, Jingyi Zhang, and Jingyan Zhang. "Study on System Recognition Method for Newton-Raphson Iterations." In 2018 International Computers, Signals and Systems Conference (ICOMSSC). IEEE, 2018. http://dx.doi.org/10.1109/icomssc45026.2018.8941745.

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Vestias, M´rio P., and Hor´cio C. Neto. "Revisiting the Newton-Raphson Iterative Method for Decimal Division." In 2011 International Conference on Field Programmable Logic and Applications (FPL). IEEE, 2011. http://dx.doi.org/10.1109/fpl.2011.33.

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Li, Yan, Yulei Luo, Buhan Zhang, and Chengxiong Mao. "A Modified Newton-Raphson Power Flow Method Considering Wind Power." In 2011 Asia-Pacific Power and Energy Engineering Conference (APPEEC). IEEE, 2011. http://dx.doi.org/10.1109/appeec.2011.5748520.

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Kim, Dohun, and Insu Kim. "The Newton-Raphson method for optimization of distributed generation resources." In 2019 IEEE Transportation Electrification Conference and Expo, Asia-Pacific (ITEC Asia-Pacific). IEEE, 2019. http://dx.doi.org/10.1109/itec-ap.2019.8903665.

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Reports on the topic "Newton-Raphson method"

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Perumalla, Kalyan S., John P. Wright, and Phani Teja Kuruganti. On the Reversibility of Newton-Raphson Root-Finding Method. Office of Scientific and Technical Information (OSTI), July 2008. http://dx.doi.org/10.2172/934800.

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Madhavan, R., M. K. Yeh, S. Kyriakides, and C. D. Babcock. L41041 Pipe Collapse Under External Pressure and Axial Tension (PUPA) Computer Program Manual. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), September 1987. http://dx.doi.org/10.55274/r0011342.

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PUPA is a computer program which predicts the critical loads of a long tube under external pressure and axial tension. The program takes into account the effect of inelastic material behaviour on collapse and could be used for tubes with diameter to thickness ratio as low as 10. The analysis is based on a principle of virtual work type of formulation and the resulting nonlinear equilibrium equations are solved using Newton-Raphson method. The model implemented considers a long tube under generalized plane strain conditions and uniform ovalization. Effect of initial ovality, residual stresses and anisotropic yielding can be included.
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Liang, Yu, Ramdev Kanapady, and Peter W. Chung. Truncated Newton-Raphson Methods for Quasicontinuum Simulations. Fort Belvoir, VA: Defense Technical Information Center, May 2006. http://dx.doi.org/10.21236/ada451394.

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AN INVESTIGATION ON THE EFFECT OF RANDOM PITTING CORROSION ON THE STRENGTH OF THE SUBSEA PIPELINE USING MONTE CARLO METHOD. The Hong Kong Institute of Steel Construction, March 2024. http://dx.doi.org/10.18057/ijasc.2024.20.1.10.

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Pitting corrosion is normally distributed randomly along the pipeline, which is the source of the uncertainty affecting the ultimate bearing capacity of the submarine pipelines. So the Monte Carlo method is employed to study the effect of pitting corrosion on the upheaval buckling behavior of the pipeline. A corroded pipeline model with randomly distributed pitting corrosion is utilized to captures the intricate realities of corrosion scenarios. Multiple corrosion models with distinct artificial patterns have been meticulously crafted. Additionally, a new pipeline element based on Euler-Bernoulli beam theory is extended considering corroded sections, pipe-soil interactions, axial load, initial imperfections, and other major factors. Moreover, the bearing capacity, vertical deformation and section stress of the pipeline under corrosion is discussed thoroughly, wherein a Newton- Raphson typed numerical analysis procedure is utilized for nonlinear analysis of the upheaval buckling of pipelines. The influence of corrosion parameters such as the corrosion depth, corrosion ratio and area loss ratio on mechanical properties of the submarine pipelines is further analyzed in detail. It’s indicated that varying patterns of corrosion distribution, despite exhibiting identical corrosion parameters, can result in distinct reduction factors and vertical buckling displacements.
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