In this paper the autoregressive filter problem for bivariate stochastic processes is reduced to a finite positive definite matrix completion problem where the completion is required to satisfy additional low rank conditions. The autoregressive filter problem may also be interpreted as a two-variable positive extension problem for trigonometric polynomials where the extension is required to be ...

We investigate a class of set constraints defined as atomic set constraints augmented with projection. This class subsumes some already studied classes such as atomic set constraints with left-hand side projection and INES constraints. All these classes enjoy the nice property that satisfiability can be tested in cubic time. This is in contrast to several other classes of set constraints, such ...

We present a family of mixed methods for linear elasticity, that yield exactly symmetric, but only weakly conforming, stress approximations. The method is presented in both two and three dimensions (on triangular and tetrahedral meshes). The method is efficiently implementable by hybridization. The degrees of freedom of the Lagrange multipliers, which approximate the displacements at the faces,...

A main result of combinatorial optimization is that clique and chromatic number of a perfect graph are computable in polynomial time (Grötschel, Lovász and Schrijver 1981). This result relies on polyhedral characterizations of perfect graphs involving the stable set polytope of the graph, a linear relaxation defined by clique constraints, and a semi-definite relaxation, the Theta-body of the gr...

Multiple orthogonal polynomials (MOP) are a non-definite version of matrix orthogonal polynomials. They are described by a Riemann-Hilbert matrix Y consisting of four blocks Y1,1, Y1,2, Y2,1 and Y2,2. In this paper, we show that detY1,1 (detY2,2) equals the average characteristic polynomial (average inverse characteristic polynomial, respectively) over the probabilistic ensemble that is associa...

For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier–series. If the density is a polynomial or a trigonometrical polynomial the coefficients of this series are simple finite terms containing only the error function, the exponential function and power...

Suppose f is a real univariate polynomial of degree D with exactly 4 monomial terms. We present an algorithm, with complexity polynomial in logD on average (relative to the stable log-uniform measure), for counting the number of real roots of f . The best previous algorithms had complexity super-linear in D. We also discuss connections to sums of squares and A-discriminants, including explicit ...

In this paper we study a new optimality criterion, the K-optimality criterion, for constructing optimal experimental designs for polynomial regression models. We focus on the pth order polynomial regression model with symmetric design space [−1, 1]. For this model, we show that there is always a symmetric K-optimal design with exactly p + 1 support points including the boundary points −1 and 1....