The use of Frege-Russell style definite descriptions for giving meaning to functions has been long established and we investigate their use in the development of Functional Programs and from these to the development of correct imperative programs. In particular, we investigate the development of a functional program for a problem, "Odd powers of odd integers", discussed by Dijsktra. If the corr...

We consider a class of matrices of the form Cn = (1/N)A 1/2 n XnBnX ∗ nA 1/2 n , where Xn is an n × N matrix consisting of i.i.d. standardized complex entries, A n is a non-negative definite Hermitian square-root of the non-negative definite matrix An, and Bn is diagonal with nonnegative diagonal entries. Under the assumption that the distribution of the eigenvalues of An and Bn converge to pro...

We consider the problem of approximating a (nonnegative definite) covariance matrix by the sum of two structured covariances –one which is diagonal and one which has low-rank. Such an additive decomposition follows the dictum of factor analysis where linear relations are sought between variables corrupted by independent measurement noise. We use as distance the Wasserstein metric between their ...

We consider a class of matrices of the form Cn = (1/N)A 1/2 n XnBnX ∗ nA 1/2 n , where Xn is an n × N matrix consisting of i.i.d. standardized complex entries, A n is a non-negative definite Hermitian square-root of the non-negative definite matrix An, and Bn is diagonal with nonnegative diagonal entries. Under the assumption that the distribution of the eigenvalues of An and Bn converge to pro...

A positive-definite transport scheme for moisture is tested in a nonhydrostatic forecast model using convection-permitting resolutions. Use of the positive-definite scheme is found to significantly reduce the large positive bias in surface precipitation forecasts found in the non-positive-definite model forecasts, in particular at high precipitation thresholds. The positive-definite scheme elim...

• Dynamic performance under various forms of disturbances. Nonlinear programming formulation for dispatch virtual inertia and damping. Semi-definite relaxation to address non-convexity. Clique decomposition approach exploit sparsity. Distributed solution based on the alternating direction method multipliers. Power grids are evolving toward 100% renewable energy interfaced by inverters. Virtual ...

We consider symplectic difference systems, which contain as special cases linear Hamiltonian difference systems and Sturm–Liouville difference equations of any even order. An associated discrete quadratic functional is important in discrete variational analysis, and while its positive definiteness has been characterized and is well understood, a characterization of its positive semidefiniteness...

We apply certain recent results pertaining to the rank minimization problem under LMI constraints to determine non-trivial lower and upper bounds for the minimal order dynamic output feedback which stabilizes a given linear time invariant plant, via Semi-Definite Programs.

A preconditioning theory for Schwarz methods is presented. The theory establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditioners. It allows for the analysis and use of non-variational and non-convergent linear methods as preconditioners for conjugate gradient methods, and it is applied to domain decomposition and ...