New perturbation analyses are presented for the block Cholesky downdating problem U T U = R T R ? X T X. These show how changes in R and X alter the Cholesky factor U. There are two main cases for the perturbation matrix R in R: (1) R is a general matrix; (2))R is an upper triangular matrix. For both cases, rst order perturbation bounds for the downdated Cholesky factor U are given using two ap...

This paper discusses the rigorous enclosure of an ellipsoid by a rectangular box, its interval hull, providing a convenient preprocessing step for constrained optimization problems. A quadratic inequality constraint with a positive definite Hessian defines an ellipsoid. The Cholesky factorization can be used to transform a strictly convex quadratic constraint into a norm inequality, for which t...

We used QCD factorization for the hadronic matrix elements to show that the existing data, in particular the branching ratios BR ( ?J/?K) and BR ( ?J/??), can be accounted for this approach. We analyzed the decay within the framework of QCD factorization. We have complete calculation of the relevant hard-scattering kernels for twist-2 and twist-3. We calculated this decays in a special scale ...

Positive semidefinite matrix factorization (PSDMF) expresses each entry of a nonnegative as the inner product two positive (psd) matrices. When all these psd matrices are constrained to be diagonal, this model is equivalent factorization. Applications include combinatorial optimization, quantum-based statistical models, and recommender systems, among others. However, despite increasing interest...

We consider several issues involved in the solution of sparse symmetric positive deenite systems by multifrontal method on distributed-memory multiprocessors. First, we present a new algorithm for computing the partial factorization of a frontal matrix on a subset of processors which signiicantly improves the performance of a distributed multifrontal algorithm previously designed. Second, new p...