Results 21 to 30 of about 25,571,312 (380)
Solving polynomial systems via homotopy continuation and monodromy [PDF]
arXiv.org, 2016 We study methods for finding the solution set of a generic system in a family of polynomial systems with parametric coefficients. We present a framework for describing monodromy based solvers in terms of decorated graphs. Under the theoretical assumption
Timothy Duff +5 more
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Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms [PDF]
Computer Methods in Applied Mechanics and Engineering, 2020 This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form.
P. Benner +4 more
semanticscholar +1 more source
Asymptotic equality of the isolated and the adiabatic susceptibility [PDF]
, 1974 Many-particle systems with a hamiltonian of the form H = A + hB, h being a parameter, are discussed. In particular, for a certain class of these systems, a criterion is derived for the asymptotic equality of the isolated and the adiabatic susceptibility ...
Caspers, W.J., Valkering, T.P.
core +8 more sources
Limit Cycles of Polynomially Integrable Piecewise Differential Systems
Axioms, 2023 In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides.
Belén García +3 more
doaj +1 more source
On the first fall degree of summation polynomials
Journal of Mathematical Cryptology, 2019 We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.
Kousidis Stavros, Wiemers Andreas
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Solving parametric polynomial systems
Journal of Symbolic Computation, 2007 The authors present a new algorithm for solving constructible or semi-algebraic systems in the indeterminates \([U,X]\) where \(U=[U_1,\dots ,U_d]\) is the set of parameters and \(X=[X_{d+1},\dots,X_n]\) the set of unknowns. To this end, they study the characterization of open subsets in the parameter space over which the number of solutions is ...
Lazard, Daniel, Rouillier, Fabrice
openaire +5 more sources
Bifurcation of critical periods of a quartic system
Electronic Journal of Qualitative Theory of Differential Equations, 2018 For the polynomial system $\dot x = ix + x \bar x ( a x^2 + b x \bar x + c \bar x^2)$ the study of critical period bifurcations is performed. Using calculations with algorithms of computational commutative algebra it is shown that at most two critical ...
Wentao Huang +3 more
doaj +1 more source
RESOLUTION OF POLYNOMIAL SYSTEMS [PDF]
Computer Mathematics, 2000 In this talk, the state of the art of solving polynomial system by algebraic methods is sketched, and the main directions where future work is needed are indicated.
openaire +2 more sources
MultiRegeneration for polynomial system solving [PDF]
ACM Communications in Computer Algebra, 2020 We demonstrate our implementation of a continuation method as described in [7] for solving polynomials systems. Given a sequence of (multi)homogeneous polynomials, the software multiregeneration outputs the respective (multi)degree in a wide range of cases and partial multidegree in all others.
Crowley, Colin +3 more
openaire +2 more sources
Certifying solutions to overdetermined and singular polynomial systems over Q [PDF]
Journal of symbolic computation, 2014 This paper is concerned with certifying that a given point is near an exact root of an overdetermined or singular polynomial system with rational coefficients. The difficulty lies in the fact that consistency of overdetermined systems is not a continuous
T. Akoglu, J. Hauenstein, Á. Szántó
semanticscholar +1 more source