Matrix analysis
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Full length article: The existence of Gaussian cubature formulas
Journal of Approximation Theory
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We consider linear functionals Ld defined over Pd ⊂ P := R-|x1,...,xn| and study how to extend Ld to a square positive L : P → R, i.e. to a linear functional L with L(p2) ≥0 for all p ∈ P. We use the connection of square positive functionals to real ideals, to orthogonal polynomials, and to moment matrices. Finally, we report how such extension techniques are used to construct and analyse cubature formulas.