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The Sylvester Equation and Kadomtsev–Petviashvili System
Published 2022-03-01Subjects: “…Sylvester equation…”
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An Extension of Sylvester’s Theorem on Arithmetic Progressions
Published 2023-06-01Subjects: “…Sylvester’s theorem…”
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Sylvester-type matrices for sparse resultants
Published 2010“…The aim of the study is to infer conditions on the class of polynomial systems that can give a resultant matrix whose size is minimized, that is an optimal or Sylvester-type sparse resultant matrix. From the work of Emiris, the ‘incremental algorithm’ has been claimed to produce optimal matrices for the class of multi-homogeneous (or multigraded) systems of special structure. …”
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Boolean Functions and Permanents of Sylvester Hadamard Matrices
Published 2021-01-01Subjects: Get full text
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Iterative methods to solve the constrained Sylvester equation
Published 2023-07-01“…In this paper, the multiple constraint least squares solution of the Sylvester equation $ AX+XB = C $ is discussed. The necessary and sufficient conditions for the existence of solutions to the considered matrix equation are given. …”
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SYLVESTER–GALLAI TYPE THEOREMS FOR APPROXIMATE COLLINEARITY
Published 2014-03-01“…This can be viewed as a stable variant of the Sylvester–Gallai theorem and its extensions. Building on the recently found connection between Sylvester–Gallai type theorems and complex locally correctable codes (LCCs), we define the new notion of stable LCCs, in which the (local) correction procedure can also handle small perturbations in the Euclidean metric. …”
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Constrainted least squares solution of Sylvester equation
Published 2021-06-01“…In this paper, we study several constrainted least squares solutions of quaternion Sylvester matrix equation. We first propose a real vector representation of quaternion matrix and study its properties. …”
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Computing Sylvester resultant matrix in hermite polynomials
Published 2019“…Then the computation of the Sylvester resultant matrix in the Hermite basis and the representation of Hermite polynomials with Sylvester type determinants are carried out. …”
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Using the Ellipsoid Method for Sylvester's Problem and its Generalization
Published 2024-03-01Subjects: Get full text
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Some results on counting roots of polynomials and the Sylvester resultant.
Published 2020-04-01“…We present two results, the first on the distribution of the roots of a polynomial over the ring of integers modulo n and the second on the distribution of the roots of the Sylvester resultant of two multivariate polynomials. …”
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The Incomplete Global GMERR Algorithm for Solving Sylvester Equation
Published 2021-02-01Subjects: Get full text
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Construction of Sylvester-Hadamard Matrices by Using Binary Code
Published 2009-04-01“…A simple method is presented which defines Sylvester-Hadamard matrices in terms of products of binary code. …”
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Gerbert of Aurillac (Pope Sylvester II) as a Clockmaker
Published 2020-09-01“…The paper analyses three preserved reports, depicting Gerbert of Aurillac (also known as: of Reims, of Ravenna, of Bobbio, and in 999–1003 as Pope Sylvester II) as a clockmaker. The Benedictine monk William of Malmesbury (died around 1143) writes about clocks Gerbert made in Reims in The History of the English Kings and describes them as arte mechanica compositum. …”
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Remedies for Misapplications of Sylvester’s Criterion: A Pedagogic Illustration
Published 2021-09-01“…Sylvester’s criterion, which verifies the positive definiteness of any real symmetric matrix by examining the signs of all leading principal minors, is an excellent analytical tool. …”
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