Relevant bibliographies by topics / Equations, Quartic. Equations, Roots of

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Equations, Quartic. Equations, Roots of'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 February 2022

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Journal articles on the topic "Equations, Quartic. Equations, Roots of"

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Kulkarni, Raghavendra G. "Intersect a quartic to extract its roots." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 16, no. 1 (2017): 73–76. http://dx.doi.org/10.1515/aupcsm-2017-0006.

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AbstractIn this note we present a new method for determining the roots of a quartic polynomial, wherein the curve of the given quartic polynomial is intersected by the curve of a quadratic polynomial (which has two unknown coefficients) at its root point; so the root satisfies both the quartic and the quadratic equations. Elimination of the root term from the two equations leads to an expression in the two unknowns of quadratic polynomial. In addition, we introduce another expression in one unknown, which leads to determination of the two unknowns and subsequently the roots of quartic polynomi
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Nickalls, R. W. D. "The quartic equation: invariants and Euler's solution revealed." Mathematical Gazette 93, no. 526 (2009): 66–75. http://dx.doi.org/10.1017/s0025557200184190.

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The central role of the resolvent cubic in the solution of the quartic was first appreciated by Leonard Euler (1707-1783). Euler's quartic solution first appeared as a brief section (§ 5) in a paper on roots of equations [1, 2], and was later expanded into a chapter entitled ‘Of a new method of resolving equations of the fourth degree’ (§§ 773-783) in his Elements of algebra [3,4].
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Riccardi, Marco. "Solution of Cubic and Quartic Equations." Formalized Mathematics 17, no. 2 (2009): 117–22. http://dx.doi.org/10.2478/v10037-009-0012-z.

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Solution of Cubic and Quartic Equations In this article, the principal n-th root of a complex number is defined, the Vieta's formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan's solution of cubic equations and the Descartes-Euler solution of quartic equations in terms of their complex coefficients are also presented [5].
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Mahmood, Munir, Sali Hammad, and Ibtihal Mahmood. "An efficient algorithm for computing the roots of general quadratic, cubic and quartic equations." International Journal of Mathematical Education in Science and Technology 45, no. 7 (2014): 1095–103. http://dx.doi.org/10.1080/0020739x.2014.902133.

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Kim, Young Ik, and Young Hee Geum. "On Constructing Two-Point Optimal Fourth-Order Multiple-Root Finders with a Generic Error Corrector and Illustrating Their Dynamics." Discrete Dynamics in Nature and Society 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/378517.

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With an error corrector via principal branch of themth root of a function-to-function ratio, we propose optimal quartic-order multiple-root finders for nonlinear equations. The relevant optimal order satisfies Kung-Traub conjecture made in 1974. Numerical experiments performed for various test equations demonstrate convergence behavior agreeing with theory and the basins of attractions for several examples are presented.
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Yang, Bo, and Jianke Yang. "General rogue waves in the three-wave resonant interaction systems." IMA Journal of Applied Mathematics 86, no. 2 (2021): 378–425. http://dx.doi.org/10.1093/imamat/hxab005.

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Abstract General rogue waves in (1+1)-dimensional three-wave resonant interaction systems are derived by the bilinear method. These solutions are divided into three families, which correspond to a simple root, two simple roots and a double root of a certain quartic equation arising from the dimension reduction, respectively. It is shown that while the first family of solutions associated with a simple root exists for all signs of the nonlinear coefficients in the three-wave interaction equations, the other two families of solutions associated with two simple roots and a double root can only ex
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Li, Hung C. "The exact proability that the roots of quadratic, cubic, and quartic equations are all real if the equation coefficients are random." Communications in Statistics - Theory and Methods 17, no. 2 (1988): 395–409. http://dx.doi.org/10.1080/03610928808829630.

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Derakhshani, Z., and M. Ghominejad. "How the spin-orbit interaction appears with the same order of a non-commutative change of framework for relativistic fermions." Modern Physics Letters A 33, no. 27 (2018): 1850158. http://dx.doi.org/10.1142/s0217732318501584.

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In this research, in a difficult but absolutely precise way of calculation, we show how a very tiny amount of a non-commutative change of quantum space would appear almost as big as a normal physical interaction, namely the Rashba spin-orbit interaction, for relativistic fermions. Hence, in order to show that, we firstly solve a relativistic equation of motion of a Dirac particle, influenced by a typical harmonic energy-dependent interaction for commutative and non-commutative frameworks via the Nikiforov–Uvarov exact approach. Then to study perturbation effects of a spin-orbit interaction, we
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Derakhshani, Z., та M. Ghominejad. "Comparing exact energy solutions of quartic eigenvalue polynomials in commutative, non-commutative and non-commutative phase frameworks for boson π−". Modern Physics Letters A 33, № 13 (2018): 1850066. http://dx.doi.org/10.1142/s0217732318500669.

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In this paper, the behavior of a Duffin–Kemmer–Petiau (DKP) boson particle in the presence of a harmonic energy-dependent interaction, under the influence of an external magnetic field is precisely studied. In order to exactly solve all equations in commutative (C), non-commutative (NC) and non-commutative phase (NCP) frameworks, the Nikiforov–Uvarov (NU) powerful exact approach is employed. All these attempts end up with solving their quartic equations, trying to find and discuss on their discriminant function [Formula: see text], in a unique way which has never been discussed for any boson i
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Kulkarni, Raghavendra G. "Picking genuine zeros of cubics in the Tschirnhaus method." Mathematical Gazette 100, no. 547 (2016): 48–53. http://dx.doi.org/10.1017/mag.2016.7.

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In 1683, the German mathematician Ehrenfried Walther von Tschirnhaus introduced a polynomial transformation which, he claimed, would eliminate all intermediate terms in a polynomial equation of any degree, thereby reducing it to a binomial form from which roots can easily be extracted [1]. As mathematicians at that time were struggling to solve quintic equations in radicals with no sign of any success, the Tschirnhaus transformation gave them some hope, and in 1786, Bring was able to reduce the general quintic to the form x5 + ax + b = 0, even though he didn't succeed in his primary mission of
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Dissertations / Theses on the topic "Equations, Quartic. Equations, Roots of"

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羅文聰 and Man-chung Law. "Small prime solutions of cubic and quartic diagonal equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1990. http://hub.hku.hk/bib/B31209221.

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Law, Man-chung. "Small prime solutions of cubic and quartic diagonal equations /." [Hong Kong] : University of Hong Kong, 1990. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12726114.

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Sletta, Ingeborg. "Finding Small Roots of Polynomial Equations Using Lattice Basis Reduction." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2009. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9832.

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SANTOS, ADILIO TITONELI DOS. "SOLVING METHODS OF ALGEBRAIC EQUATIONS AND ANALYSIS OF THE ROOTS OF POLYNOMIAL FUNCTIONS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32358@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>O trabalho apresentou as soluções de equações algébricas polinomiais por radicais e operações elementares nos coeficientes com a pesquisa baseada em livros e artigos; buscou explorar as diversas ideias desenvolvidas nas demonstrações, discussões sobre os casos e os artifícios engenhosos envolvidos, além de algumas demonstrações independentes; foram tratados ainda, os casos especiais onde as raízes estão sujeitas a condições pré estabelecidas e os coeficientes obedecem a uma dad
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Paschoa, Vanessa Gonçalves 1986. "Zeros de polinômios ortogonais de variável discreta." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306957.

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Orientadores: Dimitar Kolev Dimitrov, Roberto Andreani<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-20T03:16:09Z (GMT). No. of bitstreams: 1 Paschoa_VanessaGoncalves_D.pdf: 5593991 bytes, checksum: 19d08bd15df6ca11bb499a3d2de6db5d (MD5) Previous issue date: 2012<br>Resumo: Neste trabalho estudamos o comportamento de zeros de polinômios ortogonais clássicos de variável discreta. Provamos que certas funções que envolvem os zeros dos polinômios de Charlier, Meixner, Kravchuck e Hahn s
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Maurício, Henrique Aparecido. "Da equação do 2º grau aos métodos numéricos para resolução de equações." Universidade Federal de Juiz de Fora (UFJF), 2013. https://repositorio.ufjf.br/jspui/handle/ufjf/2360.

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Submitted by isabela.moljf@hotmail.com (isabela.moljf@hotmail.com) on 2016-08-17T15:13:07Z No. of bitstreams: 1 henriqueaparecidomauricio.pdf: 1550308 bytes, checksum: 40ef8921ad354064d383770f1e641b48 (MD5)<br>Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-08-18T12:09:42Z (GMT) No. of bitstreams: 1 henriqueaparecidomauricio.pdf: 1550308 bytes, checksum: 40ef8921ad354064d383770f1e641b48 (MD5)<br>Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-08-18T12:10:38Z (GMT) No. of bitstreams: 1 henriqueaparecidomau
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Holgado, Henrique Semensato. "Da solubilidade por meio de radicais à métodos alternativos – determinando as raízes polinomiais." Universidade Federal de Goiás, 2016. http://repositorio.bc.ufg.br/tede/handle/tede/6273.

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Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2016-09-23T11:38:00Z No. of bitstreams: 2 Dissertação - Henrique Semensato Holgado - 2016.pdf: 5760137 bytes, checksum: 77e1c33f0f094d1dbba9d61044280aa8 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-09-26T12:08:12Z (GMT) No. of bitstreams: 2 Dissertação - Henrique Semensato Holgado - 2016.pdf: 5760137 bytes, checksum: 77e1c33f0f094d1dbba9d61044280aa8 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<
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Chang, Jen-Chien Jack. "Implicit solid modeling using interval methods /." Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/10690.

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Carraschi, Jonas Eduardo. "Equações polinomiais." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-07072014-141824/.

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Estudamos neste trabalho as equações polinomiais em sua abrangência: quadráticas, cúbicas e quárticas por diversos métodos clássicos, a limitação das raízes, resultados sobre equações polinomiais com coeficientes reais e inteiros, entre outros<br>We studied in this work polynomial equations in a wide reach: quadratic, cubic and quartic polynomials by several classical methods, the boundness of roots, results about polynomial equations with real and integer coefficients, among other results
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Hirota, Eduardo Koiti. "Técnica de perturbação utilizada para solução numérica de equações do 2º e 3º graus." Universidade Federal de Goiás, 2014. http://repositorio.bc.ufg.br/tede/handle/tede/4022.

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Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2015-01-30T10:49:22Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação_Eduardo Koiti Hirota - 2014.pdf: 894506 bytes, checksum: 39a1f1c9a2e91954ecfdd1ef0513c5c0 (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-30T13:05:19Z (GMT) No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação_Eduardo Koiti Hirota - 2014.pdf: 894506 bytes, checksum: 39a1f1c9a2e91954ecfdd1ef0513c5c0 (MD5)<br>Ma
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Books on the topic "Equations, Quartic. Equations, Roots of"

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Beyond the quartic equation. Birkhäuser, 1996.

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Beyond the quartic equation. Birkhäuser, 2009.

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Numerical methods for roots of polynomials. Elsevier, 2007.

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The Fourier-analytic proof of quadratic reciprocity. John Wiley & Sons, 2000.

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Point estimation of root finding methods. Springer, 2008.

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Young, George Paxton. Forms, necessary and sufficient, of the roots of pure uni-serial abelian equations. s.n., 1993.

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Young, J. R. 1799. Researches respecting the imaginary roots of numerical equations: Being a continuation of ... Nabu Press, 2010.

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Saylor, Paul E. Computing the roots of complex orthogonal and kernel polynomials. Dept. of Computer Science, University of Illinois at Urbana-Champaign, 1986.

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Bardy, Nicole. Systèmes de racines infinis. Société mathématique de France, 1996.

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Bluston, H. S. Algebraic applications of the Spectrum/Spectrum plus microcomputers: How to solve simultaneous equations, sum series numerically, obtain complex roots of quadratic equations, test random numbers, store alphabetical data. Energy Consultancy, 1985.

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Book chapters on the topic "Equations, Quartic. Equations, Roots of"

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King, R. Bruce. "The Kiepert Algorithm for Roots of the General Quintic Equation." In Beyond the Quartic Equation. Birkhäuser Boston, 2008. http://dx.doi.org/10.1007/978-0-8176-4849-7_6.

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Gaál, István. "Quartic Fields." In Diophantine Equations and Power Integral Bases. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-23865-0_9.

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Gaál, István. "Quartic Fields." In Diophantine Equations and Power Integral Bases. Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0085-7_6.

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Gaál, István. "Quartic Relative Extensions." In Diophantine Equations and Power Integral Bases. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-23865-0_14.

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King, R. Bruce. "Algebraic Equations Soluble by Radicals." In Beyond the Quartic Equation. Birkhäuser Boston, 2008. http://dx.doi.org/10.1007/978-0-8176-4849-7_5.

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Anglin, W. S., and J. Lambek. "The Cubic and Quartic Equations." In The Heritage of Thales. Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-0803-7_26.

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Aka, Menny, Manfred Einsiedler, and Thomas Ward. "Cubic and Quartic Diophantine Equations." In Springer Undergraduate Mathematics Series. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-55233-6_6.

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Oliveira, Carlos. "Calculating Roots of Equations." In Practical C++ Financial Programming. Apress, 2015. http://dx.doi.org/10.1007/978-1-4302-6716-4_9.

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Oliveira, Carlos. "Calculating Roots of Equations." In Practical C++20 Financial Programming. Apress, 2021. http://dx.doi.org/10.1007/978-1-4842-6834-6_9.

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King, R. Bruce. "The Symmetry of Equations: Galois Theory and Tschirnhausen Transformations." In Beyond the Quartic Equation. Birkhäuser Boston, 2008. http://dx.doi.org/10.1007/978-0-8176-4849-7_3.

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Conference papers on the topic "Equations, Quartic. Equations, Roots of"

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Botta, Vanessa. "Roots of Some Trinomial Equations." In CNMAC 2016 - XXXVI Congresso Nacional de Matemática Aplicada e Computacional. SBMAC, 2017. http://dx.doi.org/10.5540/03.2017.005.01.0024.

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Walsh, P. G., and Takao Komatsu. "Recent Progress on Certain Quartic Diophantine Equations." In DIOPHANTINE ANALYSIS AND RELATED FIELDS: DARF 2007/2008. AIP, 2008. http://dx.doi.org/10.1063/1.2841908.

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Meng, Aiguo. "A Novel Method Finding Multiple Roots of Nonlinear Equations." In 2009 Second International Conference on Intelligent Computation Technology and Automation. IEEE, 2009. http://dx.doi.org/10.1109/icicta.2009.834.

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Hong-bin, Zhou. "A Novel Method Finding Multiple Roots of Nonlinear Equations." In 2009 Fifth International Conference on Natural Computation. IEEE, 2009. http://dx.doi.org/10.1109/icnc.2009.528.

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Lipkin, Harvey. "On Trigonometric Formulations of Polynomial Equations." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99695.

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The displacement analysis of open and closed kinematic chains is based on polynomial equations whose variables are functions of relative joint displacements. The objective of this paper is to investigate new and interesting properties of the transformations between the canonical cosine-sine polynomials and the even degree tan-half angle polynomials associated with displacement kinematics. Using a homogeneous coordinate formulation, it is shown that the coefficients of the polynomials are linearly related by a projective transformation whose elements can be defined recursively. The canonical co
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Zhou, Yongquan, and Delong Guo. "Finding Roots of Complex Chemistry Equations Based on Evolution Strategies." In 2008 Fourth International Conference on Natural Computation. IEEE, 2008. http://dx.doi.org/10.1109/icnc.2008.178.

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Kanno, Masaaki, Kazuhiro Yokoyama, Hirokazu Anai, and Shinji Hara. "Solution of algebraic riccati equations using the sum of roots." In the 2009 international symposium. ACM Press, 2009. http://dx.doi.org/10.1145/1576702.1576733.

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Porsani, Milton, Tad J. Ulrych, Jonilton Pessoa, W. Scott, P. Leaney, and Oliver G. Jensen. "Extended Yule‐Walker equations, nonwhite deconvolution and roots of polynomials." In SEG Technical Program Expanded Abstracts 1989. Society of Exploration Geophysicists, 1989. http://dx.doi.org/10.1190/1.1889538.

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Rabago, Julius Fergy T., and Jerico B. Bacani. "Steffensen’s analogue for approximating roots of p-adic polynomial equations." 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/10.1063/1.4965402.

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LUZYANINA, T., and D. ROOSE. "APPROXIMATION OF THE CHARACTERISTIC ROOTS OF INTEGRAL EQUATIONS WITH DISTRIBUTED DELAYS." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0127.

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Reports on the topic "Equations, Quartic. Equations, Roots of"

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Subrahmanyam, M. B. Roots of Certain Transcendental Equations for Elastic Angular Regions. Defense Technical Information Center, 1998. http://dx.doi.org/10.21236/ada368632.

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