Relevant bibliographies by topics / Solving polynomial systems of equations

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

Academic literature on the topic 'Solving polynomial systems of equations'

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Published: 3 June 2025
Last updated: 6 July 2025

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Journal articles on the topic "Solving polynomial systems of equations"

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Manocha, D. "Solving systems of polynomial equations." IEEE Computer Graphics and Applications 14, no. 2 (1994): 46–55. http://dx.doi.org/10.1109/38.267470.

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Moszyński, Krzysztof. "Remarks on polynomial methods for solving systems of linear algebraic equations." Applications of Mathematics 37, no. 6 (1992): 419–36. http://dx.doi.org/10.21136/am.1992.104521.

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LLIBRE, JAUME, and CLAUDIA VALLS. "POLYNOMIAL FIRST INTEGRALS FOR THE CHEN AND LÜ SYSTEMS." International Journal of Bifurcation and Chaos 22, no. 11 (2012): 1250262. http://dx.doi.org/10.1142/s0218127412502628.

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We characterize all the values of the parameters for which the Chen and Lü systems have polynomial first integrals by using weight homogeneous polynomials and the method of characteristics for solving partial differential equations. We improve previous results which were not complete.
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Wang, Dongming. "Solving polynomial equations: Characteristic sets and triangular systems." Mathematics and Computers in Simulation 42, no. 4-6 (1996): 339–51. http://dx.doi.org/10.1016/s0378-4754(96)00008-0.

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Serdyukova, S. I. "Solving large systems of polynomial equations using REDUCE." Programming and Computer Software 26, no. 1 (2000): 28–29. http://dx.doi.org/10.1007/bf02759175.

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Chukanov, Sergei Nikolaevich, and Ilya Stanislavovich Chukanov. "The Investigation of Nonlinear Polynomial Control Systems." Modeling and Analysis of Information Systems 28, no. 3 (2021): 238–49. http://dx.doi.org/10.18255/1818-1015-2021-3-238-249.

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The paper considers methods for estimating stability using Lyapunov functions, which are used for nonlinear polynomial control systems. The apparatus of the Gro¨bner basis method is used to assess the stability of a dynamical system. A description of the Gro¨bner basis method is given. To apply the method, the canonical relations of the nonlinear system are approximated by polynomials of the components of the state and control vectors. To calculate the Gro¨bner basis, the Buchberger algorithm is used, which is implemented in symbolic computation programs for solving systems of nonlinear polynomial equations. The use of the Gro¨bner basis for finding solutions of a nonlinear system of polynomial equations is considered, similar to the application of the Gauss method for solving a system of linear equations. The equilibrium states of a nonlinear polynomial system are determined as solutions of a nonlinear system of polynomial equations. An example of determining the equilibrium states of a nonlinear polynomial system using the Gro¨bner basis method is given. An example of finding the critical points of a nonlinear polynomial system using the Gro¨bner basis method and the Wolfram Mathematica application software is given. The Wolfram Mathematica program uses the function of determining the reduced Gro¨bner basis. The application of the Gro¨bner basis method for estimating the attraction domain of a nonlinear dynamic system with respect to the equilibrium point is considered. To determine the scalar potential, the vector field of the dynamic system is decomposed into gradient and vortex components. For the gradient component, the scalar potential and the Lyapunov function in polynomial form are determined by applying the homotopy operator. The use of Gro¨bner bases in the gradient method for finding the Lyapunov function of a nonlinear dynamical system is considered. The coordination of input-output signals of the system based on the construction of Gro¨bner bases is considered.
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Raghavan, M., and B. Roth. "Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot Manipulators." Journal of Mechanical Design 117, B (1995): 71–79. http://dx.doi.org/10.1115/1.2836473.

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Problems in mechanisms analysis and synthesis and robotics lead naturally to systems of polynomial equations. This paper reviews the state of the art in the solution of such systems of equations. Three well-known methods for solving systems of polynomial equations, viz., Dialytic Elimination, Polynomial Continuation, and Grobner bases are reviewed. The methods are illustrated by means of simple examples. We also review important kinematic analysis and synthesis problems and their solutions using these mathematical procedures.
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Raghavan, M., and B. Roth. "Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot Manipulators." Journal of Vibration and Acoustics 117, B (1995): 71–79. http://dx.doi.org/10.1115/1.2838679.

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Problems in mechanisms analysis and synthesis and robotics lead naturally to systems of polynomial equations. This paper reviews the state of the art in the solution of such systems of equations. Three well-known methods for solving systems of polynomial equations, viz., Dialytic Elimination, Polynomial Continuation, and Grobner bases are reviewed. The methods are illustrated by means of simple examples. We also review important kinematic analysis and synthesis problems and their solutions using these mathematical procedures.
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Barotov, Dostonjon Numonjonovich, and Ruziboy Numonjonovich Barotov. "Polylinear Transformation Method for Solving Systems of Logical Equations." Mathematics 10, no. 6 (2022): 918. http://dx.doi.org/10.3390/math10060918.

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In connection with applications, the solution of a system of logical equations plays an important role in computational mathematics and in many other areas. As a result, many new directions and algorithms for solving systems of logical equations are being developed. One of these directions is transformation into the real continuous domain. The real continuous domain is a richer domain to work with because it features many algorithms, which are well designed. In this study, firstly, we transformed any system of logical equations in the unit n-dimensional cube Kn into a system of polylinear–polynomial equations in a mathematically constructive way. Secondly, we proved that if we slightly modify the system of logical equations, namely, add no more than one special equation to the system, then the resulting system of logical equations and the corresponding system of polylinear–polynomial equations in Kn+1 is equivalent. The paper proposes an algorithm and proves its correctness. Based on these results, further research plans are developed to adapt the proposed method.
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Rojas, J. Maurice, and Yuyu Zhu. "A complexity chasm for solving sparse polynomial equations over p -adic fields." ACM Communications in Computer Algebra 54, no. 3 (2020): 86–90. http://dx.doi.org/10.1145/3457341.3457343.

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The applications of solving systems of polynomial equations are legion: The real case permeates all of non-linear optimization as well as numerous problems in engineering. The p -adic case leads to many classical questions in number theory, and is close to many applications in cryptography, coding theory, and computational number theory. As such, it is important to understand the complexity of solving systems of polynomial equations over local fields. Furthermore, the complexity of solving structured systems --- such as those with a fixed number of monomial terms or invariance with respect to a group action --- arises naturally in many computational geometric applications and is closely related to a deeper understanding of circuit complexity (see, e.g., [8]). Clearly, if we are to fully understand the complexity of solving sparse polynomial systems, then we should at least be able to settle the univariate case, e.g., classify when it is possible to separate and approximate roots in deterministic time polynomial in the input size.
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Dissertations / Theses on the topic "Solving polynomial systems of equations"

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Wise, Steven M. "POLSYS_PLP: A Partitioned Linear Product Homotopy Code for Solving Polynomial Systems of Equations." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36933.

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Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years of development, homotopy path trackers based on probability-one homotopy methods are reliable and fast. Now, theoretical advances reducing the number of homotopy paths that must be tracked, and in the handling of singular solutions, have made probability-one homotopy methods even more practical. This thesis describes the theory behind and performance of the new code POLSYS_PLP, which consists of Fortran 90 modules for finding all isolated solutions of a complex coefficient polynomial system of equations by a probability-one homotopy method. The package is intended to be used in conjunction with HOMPACK90, and makes extensive use of Fortran 90 derived data types to support a partitioned linear product (PLP) polynomial system structure. PLP structure is a generalization of m-homogeneous structure, whereby each component of the system can have a different m-homogeneous structure. POLSYS_PLP employs a sophisticated power series end game for handling singular solutions, and provides support for problem definition both at a high level and via hand-crafted code. Different PLP structures and their corresponding Bezout numbers can be systematically explored before committing to root finding.<br>Master of Science
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Bard, Gregory V. "Algorithms for solving linear and polynomial systems of equations over finite fields with applications to cryptanalysis." College Park, Md. : University of Maryland, 2007. http://hdl.handle.net/1903/7202.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2007.<br>Thesis research directed by: Applied Mathematics and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Mohamed, Mohamed Saied Emam. "Improved Strategies for Solving Multivariate Polynomial Equation Systems over Finite Fields." Phd thesis, TU Darmstadt, 2011. https://tuprints.ulb.tu-darmstadt.de/2622/4/Mohamed-Diss.pdf.

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One of the important research problems in cryptography is the problem of solving multivariate polynomial equations over finite fields. The hardness of solving this problem is the measure of the security of many public key cryptosystems as well as of many symmetric cryptosystems, like block and stream ciphers. In recent years, algebraic cryptanalysis has been presented as a method of attacking cryptosystems. This method consists in solving multivariate polynomial systems. Therefore, developing algorithms for solving such systems is a hot research topic. Over the recent years, several algorithms have been proposed to solve multivariate polynomial systems over finite fields. A very promising type of these algorithms is based on enlarging a system by generating additional equations and using linear algebra techniques to obtain a solution. Theoretical complexity estimates have shown that algebraic attacks made using these algorithms are infeasible for many realistic applications. This is due to the fact that, in many practical cases, the computations made by these algorithms require a lot of time and memory resources. A big challenge is to improve this algorithm in order to be able to use the limited available memory and time resources to solve large multivariate polynomial systems which exist in practice. In this thesis we propose strategies to improve the enlargement step of these algorithms. We apply these strategies to the well studied XL algorithm, due to its simple structure, and show that combining these strategies with XL makes it highly competitive to the state-of-the-art algorithms. In 2006, Jintai Ding presented the concept of mutant polynomials . Mutants are polynomials of a lower degree than expected that appear during the linear algebra step of XL. The MutantXL algorithm presented in this thesis uses the concept of mutants to improve the solving process of the XL algorithm. The MXL2 algorithm is introduced as an improved version of the MutantXL algorithm by developing a partial enlargement strategy. Specifically, we modify MutantXL in a way such that when it enlarges the system, it partitions the set of polynomials of the maximal degree D into some subsets using a special criteria. After that it explores this set of polynomials, one subset at a time, without being forced to store the whole set at once. This results in solving systems with fewer number of enlarged polynomials than MutantXL. The main drawback of MXL2, as well as XL and MutantXL algorithms, is that it can solve only systems having a unique solution. In order to solve systems with a finite number of solutions, we present a new sufficient condition for a set of polynomials to be a Gröbner basis . We used this new condition as a termination criteria for the MXL2 algorithm. This modification together with further improvements to the enlargement step of MXL2 are introduced in the MXL3 algorithm for computing Gröbner bases. This thesis also introduces the MGB algorithm which uses a flexible partial enlargement strategy to provide an important improvement to MXL3. The preliminary study presented at the end of the thesis suggests a new upper bound for the complexity of computing Gröbner bases which motivates thinking of new paradigms for estimating the complexity of Gröbner bases computation. The results in this thesis show that the proposed strategies dramatically improve the performance of the XL algorithm and, moreover, introduce algorithms that outperform Magma’s implementation of F4, one of the currently most efficient algorithms, in terms of time and memory consumption in many cases. Moreover, an adapted version of MutantXL is used to attack the MQQ cryptosystem faster and uses less memory than attacks using F4.
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Mohamed, Mohamed Saied Emam [Verfasser], Johannes [Akademischer Betreuer] Buchmann, and Jintai [Akademischer Betreuer] Ding. "Improved Strategies for Solving Multivariate Polynomial Equation Systems over Finite Fields / Mohamed Saied Emam Mohamed. Betreuer: Johannes Buchmann ; Jintai Ding." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2011. http://d-nb.info/1105562581/34.

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Vu, Thi Xuan. "Homotopy algorithms for solving structured determinantal systems." Electronic Thesis or Diss., Sorbonne université, 2020. http://www.theses.fr/2020SORUS478.

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Les systèmes polynomiaux multivariés apparaissant dans de nombreuses applications ont des structures spéciales et les systèmes invariants apparaissent dans un large éventail d'applications telles que dans l’optimisation polynomiale et des questions connexes en géométrie algébrique réelle. Le but de cette thèse est de fournir des algorithmes efficaces pour résoudre de tels systèmes structurés. Afin de résoudre le premier type de systèmes, nous concevons des algorithmes efficaces en utilisant les techniques d’homotopie symbolique. Alors que les méthodes d'homotopie, à la fois numériques et symboliques, sont bien comprises et largement utilisées dans la résolution de systèmes polynomiaux pour les systèmes carrés, l'utilisation de ces méthodes pour résoudre des systèmes surdéterminés n'est pas si claire. Hors, les systèmes déterminants sont surdéterminés avec plus d'équations que d'inconnues. Nous fournissons des algorithmes d'homotopie probabilistes qui tirent parti de la structure déterminantielle pour calculer des points isolés dans les ensembles des zéros de tels systèmes. Les temps d'exécution de nos algorithmes sont polynomiaux dans la somme des multiplicités des points isolés et du degré de la courbe d'homotopie. Nous donnons également des bornes sur le nombre de points isolés que nous devons calculer dans trois contextes: toutes les termes de l'entrée sont dans des anneaux polynomiaux classiques, tous ces polynômes sont creux, et ce sont des polynômes à degrés pondérés. Dans la seconde moitié de la thèse, nous abordons le problème de la recherche de points critiques d'une application polynomiale symétrique sur un ensemble algébrique invariant. Nous exploitons les propriétés d'invariance de l'entrée pour diviser l'espace de solution en fonction des orbites du groupe symétrique. Cela nous permet de concevoir un algorithme qui donne une description triangulaire de l'espace des solutions et qui s'exécute en temps polynomial dans le nombre de points que nous devons calculer. Nos résultats sont illustrés par des applications à l'étude d'ensembles algébriques réels définis par des systèmes polynomiaux invariants au moyen de la méthode des points critiques<br>Multivariate polynomial systems arising in numerous applications have special structures. In particular, determinantal structures and invariant systems appear in a wide range of applications such as in polynomial optimization and related questions in real algebraic geometry. The goal of this thesis is to provide efficient algorithms to solve such structured systems. In order to solve the first kind of systems, we design efficient algorithms by using the symbolic homotopy continuation techniques. While the homotopy methods, in both numeric and symbolic, are well-understood and widely used in polynomial system solving for square systems, the use of these methods to solve over-detemined systems is not so clear. Meanwhile, determinantal systems are over-determined with more equations than unknowns. We provide probabilistic homotopy algorithms which take advantage of the determinantal structure to compute isolated points in the zero-sets of determinantal systems. The runtimes of our algorithms are polynomial in the sum of the multiplicities of isolated points and the degree of the homotopy curve. We also give the bounds on the number of isolated points that we have to compute in three contexts: all entries of the input are in classical polynomial rings, all these polynomials are sparse, and they are weighted polynomials. In the second half of the thesis, we deal with the problem of finding critical points of a symmetric polynomial map on an invariant algebraic set. We exploit the invariance properties of the input to split the solution space according to the orbits of the symmetric group. This allows us to design an algorithm which gives a triangular description of the solution space and which runs in time polynomial in the number of points that we have to compute. Our results are illustrated by applications in studying real algebraic sets defined by invariant polynomial systems by the means of the critical point method
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Paramanathan, Pamini. "Systems of polynomial equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ64880.pdf.

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Vanatta, Natalie. "Solving multi-variate polynomial equations in a finite field." Monterey, California: Naval Postgraduate School, 2013. http://hdl.handle.net/10945/34756.

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Approved for public release; distribution is unlimited<br>Solving large systems of multivariate polynomial equations is an active area of mathematical research, as these polynomials are used in many fields of science. The objective of this research is to advance the development of algebraic methods to attack the mathematical foundations of modern-day encryption methods, which can be modeled as a system of multivariate polynomial equations over a finite field. Our techniques overcome the limitations of previous methods. Additionally, a model is proposed to estimate the time required to solve large systems with our methods. All of these elements were tested successfully on AES and its predecessor, Square. The results showed our techniques to be comparable with a brute force technique. To the best of our knowledge, no other purely algebraic attack on AES has been shown to be this efficient.
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Stoffel, Joshua David. "Lagrange-Chebyshev Based Single Step Methods for Solving Differential Equations." University of Akron / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=akron1335299082.

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Parts, Inga. "Piecewise polynomial collocation methods for solving weakly singular integro-differential equations /." Online version, 2005. http://dspace.utlib.ee/dspace/bitstream/10062/851/5/parts.pdf.

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Cifuentes, Pardo Diego Fernando. "Exploiting chordal structure in systems of polynomial equations." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/92972.

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Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Cataloged from student-submitted PDF version of thesis.<br>Includes bibliographical references (pages 79-81).<br>Chordal structure and bounded treewidth allow for efficient computation in linear algebra, graphical models, constraint satisfaction and many other areas. Nevertheless, it has not been studied whether chordality might also help solve systems of polynomials. We propose a new technique, which we refer to as chordal elimination, that relies in elimination theory and Gröbner bases. Chordal elimination can be seen as a generalization of sparse linear algebra. Unlike the linear case, the elimination process may not be exact. Nonetheless, we show that our methods are well-behaved for a large family of problems. We also use chordal elimination to obtain a good sparse description of a structured system of polynomials. By maintaining the graph structure in all computations, chordal elimination can outperform standard Gröbner basis algorithms in many cases. In particular, its computational complexity is linear for a restricted class of ideals. Chordal structure arises in many relevant applications and we propose the first method that takes full advantage of it. We demonstrate the suitability of our methods in examples from graph colorings, cryptography, sensor localization and differential equations.<br>by Diego Fernando Cifuentes Pardo.<br>S.M.
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Books on the topic "Solving polynomial systems of equations"

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1962-, Sturmfels Bernd, ed. Solving systems of polynomial equations. American Mathematical Society, 2002.

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Alexander, Morgan. Solving polynomial systems using continuation for engineering and scientific problems. Prentice-Hall, 1987.

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Sidi, Avram. Efficient implementation of minimal polynominal and reduced rank extrapolation methods. NASA Lewis Research Center, Institute for Computational Mechanics in Propulsion, 1990.

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Bronstein, Manuel, Arjeh M. Cohen, Henri Cohen, et al., eds. Solving Polynomial Equations. Springer-Verlag, 2005. http://dx.doi.org/10.1007/b138957.

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Wen-tsün, Wu. Mathematics mechanization: Mechanical geometry theorem-proving, mechanical geometry problem-solving, and polynomial equations-solving. Kluwer Academic Publishers, 2000.

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Gruevski, Trpe. Algorithms for solving the polynomial algebraic equations of any power. Company Samojlik, 2000.

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Bernd, Fischer. Polynomial based iteration methods for symmetric linear systems. Society for Industrial and Applied Mathematics, 2011.

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Greenbaum, Anne. Iterative methods for solving linear systems. Society for Industrial and Applied Mathematics, 1997.

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Pielczyk, Andreas. Numerical methods for solving systems of quasidifferentiable equations. A. Hain, 1991.

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Hallett, Andrew Hughes. Hybrid algorithms with automatic switching for solving nonlinear equation systems. Dept. of Economics, Fraser of Allander Institute, University of Strathclyde, 1996.

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Book chapters on the topic "Solving polynomial systems of equations"

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Mishra, Bhubaneswar. "Solving Systems of Polynomial Equations." In Algorithmic Algebra. Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-4344-1_4.

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Sommese, Andrew J., Jan Verschelde, and Charles W. Wampler. "Solving Polynomial Systems Equation by Equation." In Algorithms in Algebraic Geometry. Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-75155-9_8.

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Joswig, Michael, and Thorsten Theobald. "Solving Systems of Polynomial Equations Using Gröbner Bases." In Universitext. Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-4817-3_10.

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Ishteva, Mariya, and Philippe Dreesen. "Solving Systems of Polynomial Equations—A Tensor Approach." In Large-Scale Scientific Computing. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-97549-4_38.

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Tu, Xinghan, and Xiaohua Peng. "Solving the System of Fuzzy Polynomial Equations." In Advances in Intelligent and Soft Computing. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14880-4_18.

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Sottile, Frank. "From Enumerative Geometry to Solving Systems of Polynomial Equations." In Computations in Algebraic Geometry with Macaulay 2. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04851-1_6.

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Courtois, Nicolas, Alexander Klimov, Jacques Patarin, and Adi Shamir. "Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations." In Advances in Cryptology — EUROCRYPT 2000. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-45539-6_27.

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Ivanyos, Gábor, and Miklos Santha. "On Solving Systems of Diagonal Polynomial Equations Over Finite Fields." In Frontiers in Algorithmics. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19647-3_12.

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Grigoriev, Dima. "Polynomial Complexity of Solving Systems of Few Algebraic Equations with Small Degrees." In Computer Algebra in Scientific Computing. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02297-0_11.

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Buchinskiy, Ivan M., Matvei V. Kotov, and Alexander V. Treier. "On the Complexity of the Problem of Solving Systems of Tropical Polynomial Equations of Degree Two." In Communications in Computer and Information Science. Springer Nature Switzerland, 2024. https://doi.org/10.1007/978-3-031-73365-9_5.

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Conference papers on the topic "Solving polynomial systems of equations"

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Widdershoven, Raphael, Nico Vervliet, and Lieven De Lathauwer. "A Bézoutian-Based Method for Solving Overdetermined Systems of Polynomial Equations." In 2024 32nd European Signal Processing Conference (EUSIPCO). IEEE, 2024. http://dx.doi.org/10.23919/eusipco63174.2024.10715262.

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Babadzanjanz, L. K., I. Yu Pototskaya, Yu Yu Pupysheva, and V. S. Korolev. "EXPENDITURE OPTIMAL CONTROL FOR A SATELLITE MOVING CLOSE TO THE LIBRATION POINT." In SGEM International Multidisciplinary Scientific GeoConference 24. STEF92 Technology, 2024. https://doi.org/10.5593/sgem2024/6.1/s28.64.

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Satellite motion control in the vicinity of the libration point with expenditure criteria is considered. Expenditure optimization is natural in the case, where it is necessary to keep mechanical system in the neighborhood of the equilibrium point for a long time. Disturbing factors from time to time distort this system unacceptably far from the equilibrium point, and we need to extinguish these deviations, using fuel or another resource, which reserves are limited. Optimization of the satellite motion control according to this criterion is important not only from the economic and technical side, but also brings an environmental effect. Features of the presented mathematical problem definition are following. While deviations from the equilibrium point are very small, its controlled motion can be by linear differential equations with constant coefficients. The admissible control is a piecewise polynomial function that blanks selected frequency components of the solution of linear equations at the terminated moment T. As the expenditure functional we use the integral of the sum of the control coordinates modules along the interval [0,T]. As the results of solving the problem, formulas and an algorithm for finding the control switching points satisfying the expenditure functional extremum necessary conditions are proposed.
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Sahba, Farshid, Amin Sahba, Rmin Sahba, and Vahideh Hashempour. "A Model Based on Genetic Algorithm for Solving Polynomial Equations." In 2024 IEEE 15th Annual Ubiquitous Computing, Electronics & Mobile Communication Conference (UEMCON). IEEE, 2024. http://dx.doi.org/10.1109/uemcon62879.2024.10754782.

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Iori, Tomoyuki. "Controlled Invariant Sets for Polynomial Systems Defined by Non-polynomial Equations." In 2024 IEEE 63rd Conference on Decision and Control (CDC). IEEE, 2024. https://doi.org/10.1109/cdc56724.2024.10886422.

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Shen, Zhan, and Kexin Li. "Analog Circuit for Solving Linear Ordinary Differential Equations." In 2024 IEEE 6th International Conference on Power, Intelligent Computing and Systems (ICPICS). IEEE, 2024. https://doi.org/10.1109/icpics62053.2024.10796335.

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Canny, J. F., E. Kaltofen, and L. Yagati. "Solving systems of nonlinear polynomial equations faster." In the ACM-SIGSAM 1989 international symposium. ACM Press, 1989. http://dx.doi.org/10.1145/74540.74556.

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Mourrain, Bernard, and Victor Y. Pan. "Asymptotic acceleration of solving multivariate polynomial systems of equations." In the thirtieth annual ACM symposium. ACM Press, 1998. http://dx.doi.org/10.1145/276698.276862.

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Zjavka, Ladislav, and Vaclav Snasel. "Composing and Solving General Differential Equations Using Extended Polynomial Networks." In 2015 International Conference on Intelligent Networking and Collaborative Systems (INCOS). IEEE, 2015. http://dx.doi.org/10.1109/incos.2015.28.

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Faugère, Jean-Charles, and Sajjad Rahmany. "Solving systems of polynomial equations with symmetries using SAGBI-Gröbner bases." In the 2009 international symposium. ACM Press, 2009. http://dx.doi.org/10.1145/1576702.1576725.

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Nor, Hafizudin Mohamad, Ahmad Izani Md. Ismail, and Ahmad Abdul Majid. "Linear fixed point function for solving system of polynomial equations." In PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4882474.

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Reports on the topic "Solving polynomial systems of equations"

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Baader, Franz, Pavlos Marantidis, and Alexander Okhotin. Approximately Solving Set Equations. Technische Universität Dresden, 2016. http://dx.doi.org/10.25368/2022.227.

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Abstract:
Unification with constants modulo the theory ACUI of an associative (A), commutative (C) and idempotent (I) binary function symbol with a unit (U) corresponds to solving a very simple type of set equations. It is well-known that solvability of systems of such equations can be decided in polynomial time by reducing it to satisfiability of propositional Horn formulae. Here we introduce a modified version of this problem by no longer requiring all equations to be completely solved, but allowing for a certain number of violations of the equations. We introduce three different ways of counting the number of violations, and investigate the complexity of the respective decision problem, i.e., the problem of deciding whether there is an assignment that solves the system with at most l violations for a given threshold value l.
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Schnabel, Robert B., and Paul D. Frank. Solving Systems of Nonlinear Equations by Tensor Methods. Defense Technical Information Center, 1986. http://dx.doi.org/10.21236/ada169927.

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Zhang, Xiaodong, Richard H. Byrd, and Robert B. Schnabel. Parallel Methods for Solving Nonlinear Block Bordered Systems of Equations. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada217062.

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Bader, Brett William. Tensor-Krylov methods for solving large-scale systems of nonlinear equations. Office of Scientific and Technical Information (OSTI), 2004. http://dx.doi.org/10.2172/919158.

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Li, Guangye. The Secant/Finite Difference Algorithm for Solving Sparse Nonlinear Systems of Equations. Defense Technical Information Center, 1986. http://dx.doi.org/10.21236/ada453093.

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Varga, Richard S. Investigation on Improved Iterative Methods for Solving Sparse Systems of Linear Equations. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada187046.

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Varga, Richard S. Investigations on Improved Iterative Methods for Solving Sparse Systems of Linear Equations. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada166170.

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Marcus, Martin H. An Improved Method for Solving Systems of Linear Equations in Frequency Response Problems. Defense Technical Information Center, 2004. http://dx.doi.org/10.21236/ada422723.

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Blue, James L. B2DE -- a program for solving systems of partial differential equations in two dimensions. National Bureau of Standards, 1986. http://dx.doi.org/10.6028/nbs.ir.86-3411.

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Dennis, Jr, Li J. E., and Guangye. The Combined Schubert/Secant Finite-Difference Algorithm for Solving Sparse Nonlinear Systems of Equations. Defense Technical Information Center, 1986. http://dx.doi.org/10.21236/ada453834.

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