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Computation of Matrix Functions
No full textTesi di Dottorato in Informatica - IV ciclo - Universita` di Pis
Almost vanishing polynomials for sets of limited precision points
No full textAbstractFrom the numerical point of view, given a set X⊂Rn of s points whose coordinates are known with only limited precision, each set X˜ of s points whose elements differ from those of X of a quantity less than data uncertainty can be considered equivalent to X. We present an algorithm that, given X and a tolerance ε on the data error, computes a set G of polynomials such that each element of G is “almost vanishing” at X and at all its equivalent sets X˜. The set G is not, in the general case, a basis of the vanishing ideal I(X). Nevertheless G can determine geometrical configurations simultaneously characterizing the set X and all its equivalent sets X˜
On error evaluation for interpolatory cubature formulae
No full textIn 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 particular the error for a special class of nodes
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