Simone Naldi

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Let <i>H</i><sub>0</sub>, &#8230;, <i>H <sub>n</sub></i> be <i>m</i> x <i>m</i> matrices with entries in <i>Q</i> and Hankel structure, i.e. constant skew diagonals. We consider the linear Hankel matrix <i>H</i>(x) = <i>H</i><sub>0</sub>+<i>x</i><sub>1</sub><i>H</i>_1+&#8230;+<i>x<sub>n</sub>H<sub>n</sub></i> and the problem of computing sample points in(More)
Let A 0 , A 1 ,. .. , A n be given square matrices of size m with rational coefficients. The paper focuses on the exact computation of one point in each connected component of the real determinantal variety {x ∈ R n : det(A 0 + x 1 A 1 + · · · + x n A n) = 0}. Such a problem finds applications in many areas such as control theory, computational geometry,(More)
Let A(x) = A 0 + x 1 A 1 + · · · + x n A n be a linear matrix, or pencil, generated by given symmetric matrices A 0 , A 1 ,. .. , A n of size m with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a convex semi-algebraic set called spectrahedron, described by a linear matrix inequality (LMI). We design an exact(More)
The problem of finding low rank m × m matrices in a real affine subspace of dimension n has many applications in information and systems theory, where low rank is synonymous of structure and parcimony. We design a symbolic computation algorithm to solve this problem efficiently, exactly and rigorously: the input are the rational coefficients of the matrices(More)
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