Blar i forfatter "Blekherman, Grigoriy"

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    • Generalized eigenvalue methods for Gaussian quadrature rules 

      Blekherman, Grigoriy; Kummer, Mario; Riener, Cordian; Schweighofer, Markus; Vinzant, Cynthia (Journal article; Tidsskriftartikkel; Peer reviewed, 2020)
      A quadrature rule of a measure <i>µ</i> on the real line represents a conic combination of finitely many evaluations at points, called nodes, that agrees with integration against <i>µ</i> for all polynomials up to some fixed degree. In this paper, we present a bivariate polynomial whose roots parametrize the nodes of minimal quadrature rules for measures on the real line. We give two symmetric ...

    • Symmetric Non-Negative Forms and Sums of Squares 

      Blekherman, Grigoriy; Riener, Cordian (Journal article; Tidsskriftartikkel; Peer reviewed, 2020-05-21)
      We study symmetric non-negative forms and their relationship with symmetric sums of squares. For a fixed number of variables <i>n</i> and degree 2<i>d</i>, symmetric non-negative forms and symmetric sums of squares form closed, convex cones in the vector space of <i>n</i>-variate symmetric forms of degree 2<i>d</i>. Using representation theory of the symmetric group we characterize both cones in a ...