Semenov's Aagorithm for solving systems of nonlinear equations

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MetadadosDescriçãoIdioma
Autor(es): dc.contributorUniversidade Estadual Paulista (UNESP)-
Autor(es): dc.creatorKozlowski, Andrzej-
Data de aceite: dc.date.accessioned2019-08-21T18:17:10Z-
Data de disponibilização: dc.date.available2019-08-21T18:17:10Z-
Data de envio: dc.date.issued2016-10-26-
Data de envio: dc.date.issued2016-10-26-
Fonte completa do material: dc.identifierhttp://acervodigital.unesp.br/handle/unesp/361915-
Fonte completa do material: dc.identifierhttp://objetoseducacionais2.mec.gov.br/handle/mec/6386-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/468121-
Descrição: dc.descriptionNonlinear Equations, Systems, roots, cubic equation, Semenov's method-
Descrição: dc.descriptionWe demonstrate the method by considering a cubic equation on the unit square in the complex plane (this is equivalent to a system of two real equations of degree 3). The coefficients of the equation are chosen using three two-dimensional sliders. Semenov's method works by decomposing the rectangle into smaller ones and then performing two tests on them. If a rectangle passes the first test, there are no roots of the equation inside the rectangle. Such a rectangle is colored yellow and eliminated from further consideration. If a rectangle passes the second test, there is either one or no roots in this rectangle. Such a rectangle is colored orange and stored for further inspection. Rectangles that fail both tests are colored blue and subdivided, and the procedure is then repeated on the resulting smaller rectangles. If the system has no multiple roots, eventually only a finite number of orange rectangles are left. The roots can now be found by using Newton's method (Mathematica's FindRoot), taking the centers of the orange rectangles as starting values. Choose an equation using the sliders, then click on the successive integers to see the result for the corresponding iteration. Continue until there are no blue rectangles left. Click on 0 before trying a different equation. If a system has a repeated root, there will always be blue rectangles around the root-
Descrição: dc.descriptionComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemática-
Publicador: dc.publisherWolfram Demonstration Project-
Relação: dc.relationSemenovsAlgorithmForSolvingSystemsOfNonlinearEquations.nbp-
Direitos: dc.rightsDemonstration freeware using Mathematica Player-
Palavras-chave: dc.subjectSemenov's method-
Palavras-chave: dc.subjectRoots-
Palavras-chave: dc.subjectNonlinear equations-
Palavras-chave: dc.subjectEducação Superior::Ciências Exatas e da Terra::Matemática::Análise Complexa-
Título: dc.titleSemenov's Aagorithm for solving systems of nonlinear equations-
Tipo de arquivo: dc.typetexto-
Aparece nas coleções:Repositório Institucional - Acervo Digital Unesp

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