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2003 (v1)PublicationUploaded on: March 25, 2023
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1993 (v1)Publication
Tesi di Dottorato in Informatica - IV ciclo - Universita` di Pisa
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2010 (v1)Publication
From the numerical point of view, given a set X, subset of R^n of s points whose coordinates are known with only limited precision, each set XP of s points whose elements differ from those of X of a quantity less than the data uncertainty can be considered equivalent to X. We present an algorithm that, given X and a tolerance on the data...
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2007 (v1)Publication
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2006 (v1)Publication
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1998 (v1)Publication
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Uploaded on: December 5, 2022 -
2015 (v1)Publication
Methods from Commutative Algebra and Numerical Analysis are combined to address a problem common to many disciplines: the estimation of the expected value of a polynomial of a random vector using a linear combination of a finite number of its values. In this work we remark on the error estimation in cubature formulæ for polynomial functions and...
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1998 (v1)Publication
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Uploaded on: December 5, 2022 -
2013 (v1)Publication
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2014 (v1)Publication
In this work we remark on the error estimation in cubature formulae. Methods from Commutative Algebra and Orthogonal Polynomial Theory are combined to address a problem common to many disciplines: the estimation of the expected value of a polynomial of a random vector using a linear combination of a finite number of its values. We study in...
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2010 (v1)Publication
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Uploaded on: April 14, 2023 -
2013 (v1)Publication
Given a finite set X of points and a tolerance epsilon representing the maximum error on the coordinates of each point, we address the problem of computing a simple polynomial f whose zero-locus Z(f) ``almost'' contains the points of X. We propose a symbolic-numerical method that, starting from the knowledge of X and epsilon, determines a...
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2016 (v1)Publication
Given a finite set of points X in R^n, one may ask for polynomials p which belong to a subspace V and which attain given values at the points of X. We focus on subspaces V of R[x_1,...,x_n], generated by low order monomials. Such V werecomputed by the BM-algorithm, which is essentially based on an LU-decomposition. In this paper we present a...
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2012 (v1)Publication
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1992 (v1)Publication
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2014 (v1)Publication
We consider the classical problem of computing the expected value of a real function f of the d-variate random variable X using cubature formulæ. We use in synergy tools from Commutative Algebra for cubature rulæ, from elementary orthogonal polynomial theory and from Probability.
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2014 (v1)Publication
Recently new class of algorithms has been developed that construct polynomials that almost vanish at a finite number of d-dimensional points D. Such polynomials can be interpreted in terms of implicit regression models of the form f(x1,..., xd) = 0, where in the regression equation there is no distinction between dependent and independent...
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2009 (v1)Publication
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Uploaded on: March 31, 2023 -
2008 (v1)Publication
Let X be a set of points whose coordinates are known with limited accuracy; our aim is to give a characterization of the vanishing ideal I(X) independent of the data uncertainty. We present a method to compute, starting from X, a polynomial basis B of I(X) which exhibits structural stability, that is, if XP is any set of points differing only...
Uploaded on: March 27, 2023