On the Positive Definiteness of Cokriging Covariance Matrices

Positive definiteness of tridiagonal matrices via the numerical range

On the positive definiteness and eigenvalues of meet and join matrices

In this paper we study the positive definiteness of meet and join matrices using a novel approach. When the set Sn is meet closed, we give a sufficient and necessary condition for the positive definiteness of the matrix (Sn)f . From this condition we obtain some sufficient conditions for positive definiteness as corollaries. We also use graph theory and show that by making some graph theoretic ...

Extending Positive Definiteness

The main result of this paper gives criteria for extendibility of mappings defined on symmetric subsets of ∗-semigroups to positive definite ones. By specifying the mappings in question we obtain new solutions of relevant issues in harmonic analysis concerning truncations of some important multivariate moment problems, like complex, two-sided complex and multidimensional trigonometric moment pr...

Maintaining the positive definiteness of the matrices in reduced secant methods for equality constrained optimization

Computational Geometry of Positive Definiteness

In matrix computations, such as in factoring matrices, Hermitian and, preferably, positive definite elements are occasionally required. Related problems can often be cast as that of existence of respective elements in a matrix subspace. For two dimensional matrix subspaces, first results in this regard are due to Finsler. To assess positive definiteness in larger dimensional cases, the task bec...