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Relevant bibliographies by topics / Number of real roots of polynomial

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Academic literature on the topic 'Number of real roots of polynomial'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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Journal articles on the topic "Number of real roots of polynomial"

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Schwarzweller, Christoph. "On Roots of Polynomials and Algebraically Closed Fields." Formalized Mathematics 25, no. 3 (2017): 185–95. http://dx.doi.org/10.1515/forma-2017-0018.

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Summary In this article we further extend the algebraic theory of polynomial rings in Mizar [1, 2, 3]. We deal with roots and multiple roots of polynomials and show that both the real numbers and finite domains are not algebraically closed [5, 7]. We also prove the identity theorem for polynomials and that the number of multiple roots is bounded by the polynomial’s degree [4, 6].

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Pongprasert, Suchada, Kanyarat Chaengsisai, Wuttichai Kaewleamthong, and Puttarawadee Sriphrom. "Real Root Polynomials and Real Root Preserving Transformations." International Journal of Mathematics and Mathematical Sciences 2021 (April 30, 2021): 1–5. http://dx.doi.org/10.1155/2021/5585480.

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Polynomials can be used to represent real-world situations, and their roots have real-world meanings when they are real numbers. The fundamental theorem of algebra tells us that every nonconstant polynomial p with complex coefficients has a complex root. However, no analogous result holds for guaranteeing that a real root exists to p if we restrict the coefficients to be real. Let n ≥ 1 and P n be the vector space of all polynomials of degree n or less with real coefficients. In this article, we give explicit forms of polynomials in P n such that all of their roots are real. Furthermore, we pr

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Borwein, Peter, and Christopher Pinner. "Polynomials With {0, +1, -1} Coefficients and a Root Close to a Given Point." Canadian Journal of Mathematics 49, no. 5 (1997): 887–915. http://dx.doi.org/10.4153/cjm-1997-047-3.

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AbstractFor a fixed algebraic number α we discuss how closely α can be approximated by a root of a {0, +1, -1} polynomial of given degree. We show that the worst rate of approximation tends to occur for roots of unity, particularly those of small degree. For roots of unity these bounds depend on the order of vanishing, k, of the polynomial at α.In particular we obtain the following. Let BN denote the set of roots of all {0, +1, -1} polynomials of degree at most N and BN(α k) the roots of those polynomials that have a root of order at most k at α. For a Pisot number α in (1, 2] we show thatand

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ALIABADI, MOHSEN. "A NOTE ON THE FUNDAMENTAL THEOREM OF ALGEBRA." Bulletin of the Australian Mathematical Society 97, no. 3 (2018): 382–85. http://dx.doi.org/10.1017/s0004972718000035.

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The algebraic proof of the fundamental theorem of algebra uses two facts about real numbers. First, every polynomial with odd degree and real coefficients has a real root. Second, every nonnegative real number has a square root. Shipman [‘Improving the fundamental theorem of algebra’, Math. Intelligencer29(4) (2007), 9–14] showed that the assumption about odd degree polynomials is stronger than necessary; any field in which polynomials of prime degree have roots is algebraically closed. In this paper, we give a simpler proof of this result of Shipman.

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Koleda, D. V. "On real algebraic numbers in which the derivative of their minimal polynomial is small." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 57, no. 2 (2021): 135–47. http://dx.doi.org/10.29235/1561-2430-2021-57-2-135-147.

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Algebraic numbers are the roots of integer polynomials. Each algebraic number α is characterized by its minimal polynomial Pα that is a polynomial of minimal positive degree with integer coprime coefficients, α being its root. The degree of α is the degree of this polynomial, and the height of α is the maximum of the absolute values of the coefficients of this polynomial. In this paper we consider the distribution of algebraic numbers α whose degree is fixed and height bounded by a growing parameter Q, and the minimal polynomial Pα is such that the absolute value of its derivative P'α (α) is b

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Farahmand, K. "Number of real roots of a random trigonometric polynomial." Journal of Applied Mathematics and Stochastic Analysis 5, no. 4 (1992): 307–13. http://dx.doi.org/10.1155/s104895339200025x.

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We study the expected number of real roots of the random equation g1cosθ+g2cos2θ+…+gncosnθ=K where the coefficients gj's are normally distributed, but not necessarily all identical. It is shown that although this expected number is independent of the means of gj, (j=1,2,…,n), it will depend on their variances. The previous works in this direction considered the identical distribution for the coefficients.

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Coelho, Terence, and Bahman Kalantari. "How many real attractive fixed points can a polynomial have?" Mathematical Gazette 103, no. 556 (2019): 65–76. http://dx.doi.org/10.1017/mag.2019.8.

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While the notion of roots of a quadratic polynomial is rudimentary in high school mathematics, that of its fixed points is uncommon. A real or complex number is a fixed point of a polynomial p (x) p (θ) = θ. The fact that the notion of fixed point of polynomials is not commonly covered in high school or undergraduate mathematics is surprising because the relevance of the fixed points of a quadratic can be demonstrated easily via iterative methods for the approximation of such numbers as , when the quadratic formula offers no remedy.

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Jensen, C. U. "On the number of real roots of a solvable polynomial." Acta Arithmetica 115, no. 3 (2004): 255–63. http://dx.doi.org/10.4064/aa115-3-6.

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Nefedov, V. N., and A. V. Zharkikh. "Algorithmization and Software Implementation of the Method of Eliminating Variables in Polynomial Optimization Problems." Моделирование и анализ данных 10, no. 1 (2020): 110–28. http://dx.doi.org/10.17759/mda.2020100107.

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The method of sequential exclusion of variables in polynomial optimization problems is considered. A number of problems are solved using this method. The practical steps of an algorithm are described, which reduces the initial polynomial optimization problem to a multi-stage branching process of obtaining a finite number of alternative problems, the output of which gives a finite set of polynomials in one variable. As a result, solving a number of polynomial problems reduces to sorting out a finite number of vectors whose components are the real roots of polynomials.

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Mehlhorn, Kurt, and Michael Sagraloff. "A deterministic algorithm for isolating real roots of a real polynomial." Journal of Symbolic Computation 46, no. 1 (2011): 70–90. http://dx.doi.org/10.1016/j.jsc.2010.09.004.

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Dissertations / Theses on the topic "Number of real roots of polynomial"

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Souter, Shantay Antionette. "Mean number of real zeros of a random trigonometric polynomial." DigitalCommons@Robert W. Woodruff Library, Atlanta University Center, 1995. http://digitalcommons.auctr.edu/dissertations/1861.

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Lin, Ching Chung, and 林景俊. "Determinate of number of real roots of polynominal equation using Strum''s Theorem with application in kinematic analysis." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/44252933766802386723.

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碩士<br>國立臺灣科技大學<br>機械工程研究所<br>83<br>The subject of this thesis is to introduce Strum''s theorem to determinate of number of real roots of polynominal eqution and apply it to kinematic analysis. We first state the basic theory of Strum;s theorem and develop a recursive formula. the recursive formula will efficientlydeterminate the coefficients of Sturm''s function. Then we apply Sturm''s theorem to analyze task space strusture, joint sapce structure and rotatability of input link.

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Νταργαράς, Κωνσταντίνος. "Το θεώρημα Tarski-Seidenberg : συνέπειες και μία διδακτική έρευνα στη θεωρία πολυωνύμων με πραγματικούς συντελεστές". Thesis, 2014. http://hdl.handle.net/10889/8216.

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To αντικείμενο μελέτης της εργασίας αυτής είναι κατά μείζονα λόγο το θεώρημα Tarski-Seidenberg. Στο πρώτο κεφάλαιο μελετάμε το κίνητρο που ώθησε τον Tarski σε αυτή την έρευνα, εξιστορούμε την πορεία της ιδέας του από την ανακάλυψη μέχρι τη δημοσίευση και έπειτα προσπαθούμε να σκιαγραφήσουμε ευκρινώς τη συνολική επίδραση του θεωρήματος στα μαθηματικά και όχι μόνο. Για την ακρίβεια, αναφερόμαστε στην πληρότητα της Ευκλείδειας γεωμετρίας ως συνέπεια του θεωρήματος, στη συμβολή του θεωρήματος στην ανάπτυξη της ημιαλγεβρικής γεωμετρίας. Στο δεύτερο κεφάλαιο αποδικνύεται το εν λόγω θεώρημα, δηλαδή ό

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Books on the topic "Number of real roots of polynomial"

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1957-, Gurvits Leonid, and Banff International Research Station for Mathematics Innovation & Discovery, eds. Randomization, relaxation, and complexity in polynomial equation solving: Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, February 28--March 5, 2010, Banff, Ontario [i.e. Alberta], Canada. American Mathematical Society, 2011.

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Germany) International Conference on p-adic Functional Analysis (13th 2014 Paderborn. Advances in non-Archimedean analysis: 13th International Conference on p-adic Functional Analysis, August 12-16, 2014, University of Paderborn, Paderborn, Germany. Edited by Glöckner Helge 1969 editor, Escassut Alain editor, and Shamseddine Khodr 1966 editor. American Mathematical Society, 2016.

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Murray, Jonathan, and Nea Ehrlich, eds. Drawn from Life. Edinburgh University Press, 2018. http://dx.doi.org/10.3366/edinburgh/9780748694112.001.0001.

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Documentary cinema has always drawn from real life. However, an increasing number of contemporary filmmakers go further still, drawing onscreen images of reality through a range of animated filmmaking techniques and aesthetics. This book is the first of its kind, exploring the field of animated documentary film from a diverse range of scholarly and practice-based perspectives. The book’s chapters explore and propose answers to a range of questions that preoccupy twenty-first-century film artists and audiences alike: What are the historical roots of animated documentary? What kinds of reasons i

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Johansen, Bruce, and Adebowale Akande, eds. Nationalism: Past as Prologue. Nova Science Publishers, Inc., 2021. http://dx.doi.org/10.52305/aief3847.

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Nationalism: Past as Prologue began as a single volume being compiled by Ad Akande, a scholar from South Africa, who proposed it to me as co-author about two years ago. The original idea was to examine how the damaging roots of nationalism have been corroding political systems around the world, and creating dangerous obstacles for necessary international cooperation. Since I (Bruce E. Johansen) has written profusely about climate change (global warming, a.k.a. infrared forcing), I suggested a concerted effort in that direction. This is a worldwide existential threat that affects every living t

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Book chapters on the topic "Number of real roots of polynomial"

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Akritas, A. G., and P. G. Bradford. "The Role of the Fibonacci Sequence in the Isolation of the Real Roots of Polynomial Equations." In Applications of Fibonacci Numbers. Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-1910-5_1.

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Richardson, Daniel. "Finding the number of distinct real roots of sparse polynomials of the form p(x,x n)." In Computational Algebraic Geometry. Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-2752-6_16.

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Ştefănescu, Doru. "Inequalities on Upper Bounds for Real Polynomial Roots." In Computer Algebra in Scientific Computing. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11870814_24.

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Qiao, Youfu, and Fuqin Zhan. "Application of the Maximum Real Roots of Matching Polynomial." In Information Computing and Applications. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-25255-6_14.

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Kanno, Masaaki, Hirokazu Anai, and Kazuhiro Yokoyama. "On the Relationship Between the Sum of Roots with Positive Real Parts and Polynomial Spectral Factorization." In Numerical Methods and Applications. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-70942-8_38.

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Zaderman, Vitaly, and Liang Zhao. "Counting Roots of a Polynomial in a Convex Compact Region by Means of Winding Number Calculation via Sampling." In Computer Algebra in Scientific Computing. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-26831-2_29.

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Bolboacă, Sorana D., and Lorentz Jäntschi. "Characteristic Polynomial in Assessment of Carbon-Nano Structures." In Sustainable Nanosystems Development, Properties, and Applications. IGI Global, 2017. http://dx.doi.org/10.4018/978-1-5225-0492-4.ch004.

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Six dodecahedrane assemblies as multiple of five and respectively six structures were constructed and investigated from the topological point of view. The investigation was conducted using characteristic polynomials, graph invariant encoding important properties of the graph of the chemical structure. The assemblies of 5, 6, 15 and 25 dodecahedranes proved to have the center in the same plane while the assemblies of 12 and 24 dodecahedranes degenerated from the planar central form to a chair conformation. Generally, the number of real roots of characteristic polynomials is equal to the number of atoms in the assembly. The obtained roots of the characteristic polynomial were split into intervals and the frequency apparition spectra were simulated. The obtained spectra were used to investigate the behavior of investigated assembly.

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Hook, D. G., and P. R. McAree. "USING STURM SEQUENCES TO BRACKET REAL ROOTS OF POLYNOMIAL EQUATIONS." In Graphics Gems. Elsevier, 1990. http://dx.doi.org/10.1016/b978-0-08-050753-8.50089-9.

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Wilkins, J. Ernest. "MEAN NUMBER OF REAL ZEROS OF A RANDOM TRIGONOMETRIC POLYNOMIAL.: II." In Topics in Polynomials of One and Several Variables and Their Applications. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814360296_0035.

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Couveignes, Jean-Marc. "Computing complex zeros of polynomials and power series." In Computational Aspects of Modular Forms and Galois Representations. Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691142012.003.0005.

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The purpose of this chapter is twofold. First, it will prove two theorems (5.3.1 and 5.4.2) about the complexity of computing complex roots of polynomials and zeros of power series. The existence of a deterministic polynomial time algorithm for these purposes plays an important role in this book. More important, it will also explain what it means to compute with real or complex data in polynomial time. The chapter first recalls basic definitions in computational complexity theory, it then deals with the problem of computing square roots. The more general problem of computing complex roots of polynomials is treated thereafter and, finally, the chapter studies the problem of finding zeros of a converging power series.

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Conference papers on the topic "Number of real roots of polynomial"

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KOSTLAN, ERIC. "ON THE EXPECTED NUMBER OF REAL ROOTS OF A SYSTEM OF RANDOM POLYNOMIAL EQUATIONS." In Proceedings of SMALEFEST 2000. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812778031_0007.

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Arikawa, Keisuke. "Symbolic Computation of Inverse Kinematics for General 6R Manipulators Based on Raghavan and Roth’s Solution." In ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/detc2020-22231.

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Abstract We discuss the symbolic computation of inverse kinematics for serial 6R manipulators with arbitrary geometries (general 6R manipulators) based on Raghavan and Roth’s solution. The elements of the matrices required in the solution were symbolically calculated. In the symbolic computation, an algorithm for simplifying polynomials upon considering the symbolic constraints (constraints of the trigonometric functions and those of the rotation matrix), a method for symbolic elimination of the joint variables, and an efficient computation of the rational polynomials are presented. The elemen

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Ren, Ping, and Clément Gosselin. "Trajectory Planning of Cable-Suspended Parallel Robots Using Interval Positive-Definite Polynomials." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-71205.

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In this paper, the dynamic point-to-point trajectory planning of cable-suspended robots is investigated. A simple planar two-degree-of-freedom (2-dof) robot is used to demonstrate the technique. In order to maintain the cables’ positive tension, a set of algebraic inequalities is derived from the dynamic model of the 2-dof robot. The trajectories are defined using parametric polynomials with the coefficients determined by the prescribed initial and final states, and the variable time duration. With the polynomials substituted into the inequality constraints, the planning problem is then conver

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Xie, Jin, Kaiyin Yan, and Yong Chen. "On Global Aspects of Real Newton’s Method in Synthesis of Linkages." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99087.

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Nonlinear equations arise from the synthesis of linkages. Newton’s method is one of the most accessible and easiest to implement of the iterative root-finding algorithms for these equations. As a discrete deterministic dynamical system, Newton’s method contains subsystems which have highly random motion. In a so-called chaotic zone, there is a rapid interchange between the basins of attraction for each root of the equation. Choosing initial points from such chaotic zone, one can obtain a certain number of roots or possible all of them under the Newton’s method. In this paper, how to locate the

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Mavroidis, Constantinos, Munshi Alam, and Eric Lee. "Analytic Geometric Design of Spatial R-R Robot Manipulators." In ASME 2000 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/detc2000/mech-14068.

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Abstract This paper studies the geometric design of spatial two degrees of freedom, open loop robot manipulators with revolute joints that perform tasks, which require the positioning of the end-effector in three spatial locations. This research is important in situations where a robotic manipulator or mechanism with a small number of joint degrees of freedom is designed to perform higher degree of freedom end-effector tasks. The loop-closure geometric equations provide eighteen design equations in eighteen unknowns. Polynomial Elimination techniques are used to solve these equations and obtai

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Di Gregorio, Raffaele. "Analytic Form Solution of the Direct Position Analysis of the SP-2RS Architectures." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57037.

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When the actuators are locked, parallel manipulators (PMs) become parallel structures, that are structures constituted by two rigid bodies (platform and base) connected by a number of kinematic chains (limbs) with only passive kinematic pairs. A set of PMs is the one collecting the manipulators (SP-2RS architectures) which become structures with one limb of type SP and two limbs of type RS (P, R and S stand for prismatic pair, revolute pair and spherical pair respectively). The analytic determination of the assembly modes of the SP-2RS structures (i.e. the solution in analytic form of the dire

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KITAOKA, YOSHIYUKI. "STATISTICAL DISTRIBUTION OF ROOTS OF A POLYNOMIAL MODULO PRIME POWERS." In The 7th China–Japan Seminar on Number Theory. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814644938_0003.

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Mantzaflaris, Angelos, Bernard Mourrain, and Elias Tsigaridas. "Continued fraction expansion of real roots of polynomial systems." In the 2009 conference. ACM Press, 2009. http://dx.doi.org/10.1145/1577190.1577207.

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Bembé, Daniel, and André Galligo. "Virtual roots of a real polynomial and fractional derivatives." In the 36th international symposium. ACM Press, 2011. http://dx.doi.org/10.1145/1993886.1993897.

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Ben-Or, M., E. Feig, D. Kozen, and P. Tiwari. "A fast parallel algorithm for determining all roots of a polynomial with real roots." In the eighteenth annual ACM symposium. ACM Press, 1986. http://dx.doi.org/10.1145/12130.12165.

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