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On the Computation of Tensor Functions under Tensor‐Tensor Multiplications with Linear Maps
ABSTRACT In this paper, we study the computation of both algebraic and non‐algebraic tensor functions under the tensor‐tensor multiplication with linear maps. In the case of algebraic tensor functions, we prove that the asymptotic exponent of both the tensor‐tensor multiplication and the tensor polynomial evaluation problem under this multiplication is
Jeong‐Hoon Ju, Susana López‐Moreno
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Polynomial algorithms for linear programming over the algebraic numbers
Proceedings of the twenty-fourth annual ACM symposium on Theory of computing - STOC '92, 1992Linear programming (LP) is the problem of maximizing \(cx\) \((c\), a fixed \(n\)-vector), subject to \(Ax \Leftarrow b\) \((A\), a fixed \(m\) by \(n\) matrix and \(b\) a fixed \(m\)-vector). The dimension of a problem instance is the total number of entries in the vectors and matrices that define the instance (above: \(mn + n + m)\).
Ilan Adler, Peter A. Beling
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A linear-algebraic method to compute polynomial PDE conservation laws
Journal of Symbolic Computation, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Boreale, M, Collodi, L
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Position–momentum decomposition of linear operators defined on algebras of polynomials
Journal of Mathematical Physics, 2021We present first a set of commutator relationships involving the joint quantum, semi-quantum, and number operators generated by a finite family of random variables, having finite moments of all orders, and show how these commutators can be used to recover the joint quantum operators from the semi-quantum operators.
A. I. Stan, G. Popa, R. Dutta
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The algebra of linear functionals on polynomials, with applications to Padé approximation
Numerical Algorithms, 1996This paper is an interesting and complete study of the algebra of linear functionals on the vector space of complex polynomials. The results obtained have application to Padé and Padé-type approximants and lead to a different procedure for increasing the order of approximations, as well as to a new formula for the relative error.
Claude Brezinski, Pascal Maroni
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Linear algebraic approach for computing polynomial resultant
1982This paper presents a linear algebraic method for computing the re sultant of two polynomials. This method is based on the computation of a determinant of order equal to the minimum of the degrees of the two giv en polynomials. This method turns out to be preferable to other known linear algebraic methods both from a computational point of view and for
Luciana Bordoni +2 more
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