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Recovering the cluster picture of a polynomial over a discretely valued field [PDF]
Royal Society Open ScienceFor [Formula: see text], a separable polynomial of degree [Formula: see text] over a discretely valued field [Formula: see text], we describe how the cluster picture of [Formula: see text] over [Formula: see text], in other words, the set of tuples ...
Lilybelle Cowland Kellock
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Quasi-polynomials of Capelli. III [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2021 In this paper polynomials of Capelli type (double and quasi-polynomials of Capelli) belonging to a free associative algebra $F\{X\cup Y\}$ considering over an arbitrary field $F$ and generated by two disjoint countable sets $X, Y ...
Antonov, Stepan Yuryevich +1 more
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Computing and using minimal polynomials [PDF]
Journal of Symbolic Computation, 2020 This is a fully revised version. To be published in Journal of Symbolic Computation, special Issue on Symbolic Computation and Satisfiability ...
John Abbott +3 more
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Approximation of the Constant in a Markov-Type Inequality on a Simplex Using Meta-Heuristics
Mathematics, 2021 Markov-type inequalities are often used in numerical solutions of differential equations, and their constants improve error bounds. In this paper, the upper approximation of the constant in a Markov-type inequality on a simplex is considered.
Grzegorz Sroka, Mariusz Oszust
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Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability
Mathematics, 2021 Some properties of generalized convexity for sets and functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is developed based on ...
Gabriela Cristescu +2 more
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On dynamics of asymptotically minimal polynomials
Journal of Approximation Theory, 2023 Minor revisions, to appear in Journal of Approximation ...
Turgay Bayraktar, Melike Efe
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On the Ehrhart Polynomial of Minimal Matroids [PDF]
Discrete & Computational Geometry, 2021 AbstractWe provide a formula for the Ehrhart polynomial of the connected matroid of size n and rank k with the least number of bases, also known as a minimal matroid. We prove that their polytopes are Ehrhart positive and $$h^*$$ h ∗ -real-rooted (and hence ...
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Application of the Lagrange-Sylvester formula to computation of the solution to state equations of fractional linear systems [PDF]
Bulletin of the Polish Academy of Sciences: Technical Sciences, 2021 The Lagrange-Sylvester formula is applied to the computation of the solutions of state equations of fractional continuous-time and discrete-time linear systems.
Tadeusz Kaczorek
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Computing Minimal Polynomials of Matrices [PDF]
LMS Journal of Computation and Mathematics, 2008 AbstractWe present and analyse a Monte-Carlo algorithm to compute the minimal polynomial of ann × nmatrix over a finite field that requiresO(n3) field operations andO(n) random vectors, and is well suited for successful practical implementation. The algorithm, and its complexity analysis, use standard algorithms for polynomial and matrix operations. We
Max Neunhöffer, Cheryl E. Praeger
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Minimizing polynomial functions [PDF]
, 2003 We compare algorithms for global optimization of polynomial functions in many variables. It is demonstrated that existing algebraic methods (Gröbner bases, resultants, homotopy methods) are dramatically outperformed by a relaxation technique, due to N.Z. Shor and the first author, which involves sums of squares and semidefinite programming.
Pablo A. Parrilo, Bernd Sturmfels
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