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Relevant bibliographies by topics / High-degree polynomials

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Academic literature on the topic 'High-degree polynomials'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 July 2025

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Journal articles on the topic "High-degree polynomials"

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Skrzipek, Michael-Ralf. "Evaluation of High Degree Polynomials." Results in Mathematics 53, no. 3-4 (2009): 427–34. http://dx.doi.org/10.1007/s00025-008-0354-9.

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Sitton, G. A., C. S. Burrus, J. W. Fox, and S. Treitel. "Factoring very-high-degree polynomials." IEEE Signal Processing Magazine 20, no. 6 (2003): 27–42. http://dx.doi.org/10.1109/msp.2003.1253552.

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Dégot, Jérôme. "Sendov conjecture for high degree polynomials." Proceedings of the American Mathematical Society 142, no. 4 (2014): 1337–49. http://dx.doi.org/10.1090/s0002-9939-2014-11888-0.

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Tao, Terence. "Sendov’s conjecture for sufficiently-high-degree polynomials." Acta Mathematica 229, no. 2 (2022): 347–92. http://dx.doi.org/10.4310/acta.2022.v229.n2.a3.

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Beletsky, Anatoly. "An Effective Algorithm for the Synthesis of Irreducible Polynomials over a Galois Fields of Arbitrary Characteristics." WSEAS TRANSACTIONS ON MATHEMATICS 20 (September 30, 2021): 508–19. http://dx.doi.org/10.37394/23206.2021.20.54.

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The known algorithms for synthesizing irreducible polynomials have a significant drawback: their computational complexity, as a rule, exceeds the quadratic one. Moreover, consequently, as a consequence, the construction of large-degree polynomials can be implemented only on computing systems with very high performance. The proposed algorithm is base on the use of so-called fiducial grids (ladders). At each rung of the ladder, simple recurrent modular computations are performers. The purpose of the calculations is to test the irreducibility of polynomials over Galois fields of arbitrary charact

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Shi, Jun, Jieqing Tan, and Li Zhang. "A Simple Method for Constructing Symmetric Subdivision Schemes with High-Degree Polynomial Reproduction." Symmetry 15, no. 12 (2023): 2202. http://dx.doi.org/10.3390/sym15122202.

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In this paper, we present an efficient method for constructing symmetric subdivision schemes reproducing high-degree polynomials, without solving a system of linear equations. Original symmetric subdivision and its deduced subdivisions have similar increasing characteristics to the family of pseudo-splines from the polynomial reproduction point of view. Several examples are given to illustrate the efficiency of the method.

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Chiang, D. "Factorization of high degree polynomials-a numerical solution." IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 43, no. 9 (1996): 792–94. http://dx.doi.org/10.1109/81.536750.

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Treitel, S., G. A. Sitton, J. W. Fox, and C. S. Burrus. "Factoring high-degree polynomials with applications to geophysics." Leading Edge 25, no. 10 (2006): 1216–19. http://dx.doi.org/10.1190/1.2360607.

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Schrade, Emanuel, Johannes Hanika, and Carsten Dachsbacher. "Sparse high-degree polynomials for wide-angle lenses." Computer Graphics Forum 35, no. 4 (2016): 89–97. http://dx.doi.org/10.1111/cgf.12952.

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Garcia, R. D. M., and C. E. Siewert. "On computing the Chandrasekhar polynomials in high order and high degree." Journal of Quantitative Spectroscopy and Radiative Transfer 43, no. 3 (1990): 201–5. http://dx.doi.org/10.1016/0022-4073(90)90052-8.

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Dissertations / Theses on the topic "High-degree polynomials"

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Jimack, Peter K. "Finite element methods using high degree piecewise polynomials on continuously deforming grids." Thesis, University of Bristol, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.330300.

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E, Michurin I. "Using newton fractals for finding polynomial roots In the complex plane." Thesis, National Aviation University, 2021. https://er.nau.edu.ua/handle/NAU/50717.

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1. Bakhvalov, N. S., Zhidkov, N. P., & Kobelkov, G. M. (Eds.) (2008). Numerical methods. (6th ed.). Moscow: BINOM. Knowledge Laboratory. 2. Bozhokin, S. V., & Parshin, D. A. (2001). Fractals and multifractals. Izhevsk: Research Center "Regular and chaotic dynamics". 3. Zadachyn, V. M., & Konyushenko, I. G. (2014). Numerical methods. Kharkiv: Ed. KhNEU them. S. Kuznets.<br>The problem of finding complex roots arises not only in algebra or number theory, but also in other fields. Various differential equations that describe physical processes: the behavior of nonlinear dynamical systems, turbu

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Strapason, Lísie Pippi Reis. "O USO DE JOGOS COMO ESTRATÉGIA DE ENSINO E APRENDIZAGEM DA MATEMÁTICA NO 1º ANO DO ENSINO MÉDIO." Universidade Franciscana, 2011. http://tede.universidadefranciscana.edu.br:8080/handle/UFN-BDTD/121.

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Made available in DSpace on 2018-06-27T19:13:08Z (GMT). No. of bitstreams: 2 Lisie Pippi Reis Strapason.pdf: 15815936 bytes, checksum: acdbd264444719c7cb3c54be6fc19f80 (MD5) Lisie Pippi Reis Strapason.pdf.jpg: 3093 bytes, checksum: eb31814671a837cb2fa782245e5e80f5 (MD5) Previous issue date: 2011-09-30<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>This study aimed to find out whether the use of games as a teaching strategy to facilitate students learning concerning to the function concept and polynomial functions of the 1st and 2nd degrees. This research was accompli

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Mesquita, Marcia Aparecida Nunes. "Ensinar e aprender funções polinomiais do 2.º grau, no ensino médio: construindo trajetórias." Pontifícia Universidade Católica de São Paulo, 2009. https://tede2.pucsp.br/handle/handle/11422.

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Made available in DSpace on 2016-04-27T16:58:59Z (GMT). No. of bitstreams: 1 Marcia Aparecida Nunes Mesquita.pdf: 3486728 bytes, checksum: e8adb59bb70b5281983a38f1e796dc67 (MD5) Previous issue date: 2009-09-30<br>Secretaria da Educação do Estado de São Paulo<br>The present work has like objective to investigating how to make constructivist perspectives of learning compatible with the planning of the teaching-learning process, in the particular case of the teaching and of the learning of polynomial functions of the second degree and to analyze the performance of Mathematic teacher with refer

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LIU, XIANG-CHUAN, and 劉湘川. "The optimal feasible high degree polynomial stein-rule estimators for gaussian linear models." Thesis, 1987. http://ndltd.ncl.edu.tw/handle/41265050281394024401.

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Books on the topic "High-degree polynomials"

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High degree interpolation polynomial in Newton form. National Aeronautics and Space Administration, Langley Research Center, 1988.

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Book chapters on the topic "High-degree polynomials"

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Chen, Xin, and Liang Feng Zhang. "Two-Server Verifiable Homomorphic Secret Sharing for High-Degree Polynomials." In Lecture Notes in Computer Science. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-62974-8_5.

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Li, Haokun, Bican Xia, and Tianqi Zhao. "Local Search for Solving Satisfiability of Polynomial Formulas." In Computer Aided Verification. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-37703-7_5.

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AbstractSatisfiability Modulo the Theory of Nonlinear Real Arithmetic, SMT(NRA) for short, concerns the satisfiability of polynomial formulas, which are quantifier-free Boolean combinations of polynomial equations and inequalities with integer coefficients and real variables. In this paper, we propose a local search algorithm for a special subclass of SMT(NRA), where all constraints are strict inequalities. An important fact is that, given a polynomial formula with n variables, the zero level set of the polynomials in the formula decomposes the n-dimensional real space into finitely many compo

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Xu, Lin, Dongdai Lin, and Xin Li. "A New Efficient Algorithm for Computing All Low Degree Annihilators of Sparse Polynomials with a High Number of Variables." In Information Security, Practice and Experience. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12827-1_10.

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Ahle, Thomas D., Michael Kapralov, Jakob B. T. Knudsen, et al. "Oblivious Sketching of High-Degree Polynomial Kernels." In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics, 2020. http://dx.doi.org/10.1137/1.9781611975994.9.

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Yang, Zhengfeng, Li Zhang, Xia Zeng, Xiaochao Tang, Chao Peng, and Zhenbing Zeng. "Hybrid Controller Synthesis for Nonlinear Systems Subject to Reach-Avoid Constraints." In Computer Aided Verification. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-37706-8_16.

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AbstractThere is a pressing need for learning controllers to endow systems with properties of safety and goal-reaching, which are crucial for many safety-critical systems. Reinforcement learning (RL) has been deployed successfully to synthesize controllers from user-defined reward functions encoding desired system requirements. However, it remains a significant challenge in synthesizing provably correct controllers with safety and goal-reaching requirements. To address this issue, we try to design a special hybrid polynomial-DNN controller which is easy to verify without losing its expressiven

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Belkić, Dževad. "Finding accurate zeros of high-degree polynomials." In Quantum-Mechanical Signal Processing and Spectral Analysis. CRC Press, 2019. http://dx.doi.org/10.1201/9780429146534-28.

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"Finding accurate zeros of high-degree polynomials." In Series in Atomic Molecular Physics. Taylor & Francis, 2004. http://dx.doi.org/10.1201/9781420033601.ch28.

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Kowalski, Marek A., Krzystof A. Sikorski, and Frank Stenger. "Splines." In Selected Topics in Approximation and Computation. Oxford University Press, 1995. http://dx.doi.org/10.1093/oso/9780195080599.003.0005.

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Spline functions are important approximation tools in numerous applications for which high degree polynomial methods perform poorly, such as in computer graphics and geometric modelling, as well as for various engineering problems—especially those involving graphing of numerical solutions and noisy data. Algorithms based on spline functions enjoy minimal approximation errors in wide classes of problems and minimal complexity bounds. In this Chapter we provide a brief introduction to basic classes of polynomial splines, B-Splines, and abstract splines. Further study of spline algorithms as appl

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Bertoni Alberto, Folgieri Raffaella, and Valentini Giorgio. "Classification of DNA microarray data with Random Projection Ensembles of Polynomial SVMs." In Frontiers in Artificial Intelligence and Applications. IOS Press, 2009. https://doi.org/10.3233/978-1-58603-984-4-60.

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In this paper we propose and experimentally analyze ensemble methods based on random projections (as feature extraction method) and SVM with polynomial kernels (as learning algorithm). We show that, under suitable conditions, polynomial kernels are approximately preserved by random projections, with a degradation related to the square of the degree of the polynomial. Experimental results with Random Subspace and Random Projection ensembles of polynomial SVMs, support the hypothesis the low degree polynomial kernels, introducing with high probability lower distortions in the projected data, are

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Fulcher, John, Ming Zhang, and Shuxiang Xu. "Application of Higher-Order Neural Networks to Financial Time-Series Prediction." In Artificial Neural Networks in Finance and Manufacturing. IGI Global, 2006. http://dx.doi.org/10.4018/978-1-59140-670-9.ch005.

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Financial time-series data is characterized by nonlinearities, discontinuities, and high-frequency multipolynomial components. Not surprisingly, conventional artificial neural networks (ANNs) have difficulty in modeling such complex data. A more appropriate approach is to apply higher-order ANNs, which are capable of extracting higher-order polynomial coefficients in the data. Moreover, since there is a one-to-one correspondence between network weights and polynomial coefficients, higher-order neural networks (HONNs) — unlike ANNs generally — can be considered open-, rather than “closed-box” s

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Conference papers on the topic "High-degree polynomials"

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Tóth, Jan, and Ondřej Kuželka. "Complexity of Weighted First-Order Model Counting in the Two-Variable Fragment with Counting Quantifiers: A Bound to Beat." In 21st International Conference on Principles of Knowledge Representation and Reasoning {KR-2023}. International Joint Conferences on Artificial Intelligence Organization, 2024. http://dx.doi.org/10.24963/kr.2024/64.

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We study the time complexity of weighted first-order model counting (WFOMC) over the logical language with two variables and counting quantifiers. The problem is known to be solvable in time polynomial in the domain size. However, the degree of the polynomial, which turns out to be relatively high for most practical applications, has never been properly addressed. First, we formulate a time complexity bound for the existing techniques for solving WFOMC with counting quantifiers. The bound is already known to be a polynomial with its degree depending on the number of cells of the input formula.

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Rocchini, Gabriele. "pH Influence on Magnetite Stability in Steam Generator Tubes." In CORROSION 1992. NACE International, 1992. https://doi.org/10.5006/c1992-92252.

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Abstract Magnetite solubility, as a function of temperature and partial hydrogen pressure and with reference to the typical conditions of the operating fluid of a steam generator of a thermal power plant, has been studied by rigorously solving the problem of chemical equilibria and adopting the scheme proposed by Sweeton and Baes. Stoichiometric calculations have proved that magnetite solubility attains its maximum value, which depends on the characteristics of the electrolytic solution, when temperature is about 100°C, independently of the type of environment. The rigorous pH calculation was

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Kaltofen, Erich, and Austin Lobo. "Factoring high-degree polynomials by the black box Berlekamp algorithm." In the international symposium. ACM Press, 1994. http://dx.doi.org/10.1145/190347.190371.

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Tao, Pen, and Zeng Zhe-zhao. "A Neural-Network Algorithm Finding Zeros of Polynomials of High Degree." In 2009 3rd International Symposium on Intelligent Information Technology Application Workshops (IITAW). IEEE, 2009. http://dx.doi.org/10.1109/iitaw.2009.70.

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Schönherr, Jürgen. "Cam Motion Synthesis for Mixed Motion Constraints Using Well-Behaved Polynomials of High Order." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/mech-1016.

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Abstract A method of describing a function by a number of successive polynomials of unrestricted and varying degree has been developed to synthesize a cam motion for mixed constraints. The algorithm is based on the expression of the coefficients of a polynomial in terms of the constraints at interval boundaries. It enables the designer to satisfy numerous motion constraints while at the same time preserving the continuity of motion derivatives up to a high order. Unconstrained boundary values are calculated automatically by using an objective function that minimizes the oscillations of a motio

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Hernandez, Gaston, and Ricardo Gavino. "Reduction of high degree characteristic polynomials to 2nd degree for infinite range of gain applying gain margins and phase margins curve." In 2006 IEEE International Symposium on Industrial Electronics. IEEE, 2006. http://dx.doi.org/10.1109/isie.2006.296029.

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Burrus, C., James Fox, Gary Sitton, and Sven Treitel. "A Parallel Version of the Lindsey-Fox algorithm for factoring High Degree Polynomials in Signal Processing." In 2006 IEEE 12th Digital Signal Processing Workshop & 4th IEEE Signal Processing Education Workshop. IEEE, 2006. http://dx.doi.org/10.1109/dspws.2006.265415.

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Pustoshilov, Aleksandr. "DETECTING CYCLE SLIPS IN CARRIER-PHASE MEASURMENTS OF NAVIGATION RECEIVER WITH HIGH STABLE REFERENCE GENERATORS." In CAD/EDA/SIMULATION IN MODERN ELECTRONICS 2021. Bryansk State Technical University, 2021. http://dx.doi.org/10.30987/conferencearticle_61c997ee595646.84715756.

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The paper shows a simple method for detecting cycle slips in the carrier-phase measurements (including single frequency measurements) of navigation receivers with highly stable (hydrogen) reference oscillators by using approximation by high-degree polynomials.

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Kuo, Y. L., and W. L. Cleghorn. "Accuracy Enhancement of Flexible Fourbar Mechanisms via the Curvature-Based Finite Element Method." In ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/detc2008-49497.

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The paper investigates accuracy enhancement of flexible four-bar mechanisms via the curvature-based finite element method. Conventionally, the displacement-based method is usually applied to solid mechanics, and it needs more elements or high-degree polynomials to obtain highly accurate solutions. The curvature-based method assumes a polynomial to approximate a curvature distribution, and the expressions are investigated to obtain the displacement and rotation distributions. During the process, the boundary conditions associated with displacement, rotation, and curvature are imposed, which lea

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Attar, Peter J., and Earl H. Dowell. "A Reduced Order System ID Approach to the Modeling of Nonlinear Structural Behavior in Aeroelasticity." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84309.

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A method is proposed for identifying a set of reduced order, nonlinear equations which describe the structural behavior of aeroelastic configurations. The strain energy of the system is written as a (polynomial) function of the structures’ modal amplitudes. The unknown coefficients of these polynomials are then computed using the strain energy data calculated from a steady state, high-order, nonlinear finite element model. The resulting strain energy expression can then be be used to develop the modal equations of motion. From these equations zero and nonzero angle of attack flutter and LCO da

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