Results 1 to 10 of about 1,823 (264)
Interpolation Polynomials and Linear Algebra
, 2022 15 ...
Askold, Khovanskii +2 more
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Symmetric functions on spaces $\ell_p(\mathbb{{R}}^n)$ and $\ell_p(\mathbb{{C}}^n)$
Karpatsʹkì Matematičnì Publìkacìï, 2020 This work is devoted to the study of algebras of continuous symmetric polynomials, that is, invariant with respect to permutations of coordinates of its argument, and of $*$-polynomials on Banach spaces $\ell_p(\mathbb{R}^n)$ and $\ell_p(\mathbb{C}^n ...
T.V. Vasylyshyn
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Computing Linear Extensions for Polynomial Posets Subject to Algebraic Constraints [PDF]
SIAM Journal on Applied Algebra and Geometry, 2021 In this paper we consider the classical problem of computing linear extensions of a given poset which is well known to be a difficult problem. However, in our setting the elements of the poset are multivariate polynomials, and only a small "admissible" subset of these linear extensions, determined implicitly by the evaluation map, are of interest. This
Shane Kepley +2 more
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Matrix approach to solve polynomial equations
Results in Applied Mathematics, 2023 Polynomials are widely employed to represent numbers derived from mathematical operations in nearly all areas of mathematics. The ability to factor polynomials entirely into linear components allows for a wide range of problem simplifications. This paper
Samir Brahim Belhaouari +2 more
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Polynomial Invariants by Linear Algebra [PDF]
, 2016 We present in this paper a new technique for generating polynomial invariants, divided in two independent parts : a procedure that reduces polynomial assignments composed loops analysis to linear loops under certain hypotheses and a procedure for generating inductive invariants for linear loops. Both of these techniques have a polynomial complexity for
Oliveira, S., Bensalem, S., Prevosto, V.
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Mathematics, 2023 In this paper, a model matching feedback law design technique is applied to a macroeconomical model. We calculate, using computational algebra methodology, which paths of government expenditure and extra taxation will lead the system to a desired dynamic
Stelios Kotsios
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Real Root Polynomials and Real Root Preserving Transformations
International Journal of Mathematics and Mathematical Sciences, 2021 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.
Suchada Pongprasert +3 more
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Some properties of shift operators on algebras generated by $*$-polynomials
Karpatsʹkì Matematičnì Publìkacìï, 2018 A $*$-polynomial is a function on a complex Banach space $X,$ which is a sum of so-called $(p,q)$-polynomials. In turn, for non-negative integers $p$ and $q,$ a $(p,q)$-polynomial is a function on $X,$ which is the restriction to the diagonal of some ...
T.V. Vasylyshyn
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Entire Analytic Functions of Unbounded Type on Banach Spaces and Their Lineability
Axioms, 2021 In the paper we establish some conditions under which a given sequence of polynomials on a Banach space X supports entire functions of unbounded type, and construct some counter examples.
Andriy Zagorodnyuk, Anna Hihliuk
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Generalized Standard Triples for Algebraic Linearizations of Matrix Polynomials
The Electronic Journal of Linear Algebra, 2021 We define generalized standard triples $\boldsymbol{X}$, $\boldsymbol{Y}$, and $L(z) = z\boldsymbol{C}_{1} - \boldsymbol{C}_{0}$, where $L(z)$ is a linearization of a regular matrix polynomial $\boldsymbol{P}(z) \in \mathbb{C}^{n \times n}[z]$, in order to use the representation $\boldsymbol{X}(z \boldsymbol{C}_{1}~-~\boldsymbol{C}_{0})^{-1}\boldsymbol{
Eunice Y.S. Chan +2 more
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