The numerical approximation of definite integrals, or quadrature, often involves the construction of an interpolant of the integrand and its subsequent integration. In the case of one dimension it is natural to rely on polynomial interpolants. However, their extension to two or more dimensions can be costly and unstable. An efficient method for computing surface integrals on the sphere is detai...

We present a new full Nesterov and Todd step infeasible interior-point algorithm for semi-definite optimization. The algorithm decreases the duality gap and the feasibility residuals at the same rate. In the algorithm, we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Every main iteration of the algorithm consists of a feasibility...

Let O be a maximal order in a definite quaternion algebra over Q of prime discriminant p, and ` a small prime. We describe a probabilistic algorithm, which for a given left O-ideal, computes a representative in its left ideal class of `-power norm. In practice the algorithm is efficient, and subject to heuristics on expected distributions of primes, runs in expected polynomial time. This breaks...

The detailed spectral structure of symmetric, algebraic, quadratic eigenvalue problems has been developed recently. In this paper we take advantage of these canonical forms to provide a detailed analysis of inverse problems of the form: construct the coefficient matrices from the spectral data including the classical eigenvalue/eigenvector data and sign characteristics for the real eigenvalues....

To make ABox reasoning scalable for large ABoxes in description logic (DL) knowledge bases, we develop a method for partitioning the ABox so that specific kinds of reasoning can be performed separately on each partition and the results trivially combined can achieve complete answers. Our method applies to SHIQ(D) knowledge bases. It first converts a DL knowledge base KB to a plain datalog progr...

In this paper, we propose a computational scheme of solving the output feedback H∞ control problem for a class of nonlinear systems with polynomial vector field. The output feedback control design problem will be decomposed into a state feedback and an output estimation problems. Resorting to higher order Lyapunov functions, two Hamilton-JacobianIsaacs (HJI) inequalities are first formulated as...

Employing the concept of termination of sequence of SDS sets to describe the positive semidefinite property of a form, we establish a necessary and sufficient condition for deciding whether a given form on Rn+ is positive semi-definite or not, and show that, for a form which is (strictly) positive definite on Rn+, the corresponding sequence of SDS sets is positively terminating. The above resul...