We have developed a highly parallel sparse Cholesky factorization algorithm that substantially improves the state of the art in parallel direct solution of sparse linear systems—both in terms of scalability and overall performance. It is a well known fact that dense matrix factorization scales well and can be implemented efficiently on parallel computers. However, it had been a challenge to dev...

In the simple assignment problem, there are n processors, m tasks, and a relation between the processors and tasks; this relation indicates the ability of the processor to perform the task. When the processors fail independently with known probabilities, two performance issues arise. First, with what probability can the operating processors all be kept busy? Second, with what probability can th...

Since it is well-known that the Vandermonde matrix is ill-conditioned, while the interpolation itself is not unstable in function space, this paper surveys the choices of other new bases. These bases are data-dependent and are categorized into discretely l2-orthonormal and continuously L2-orthonormal bases. The first one construct a unitary Gramian matrix in the space l2(X) while the late...

This work investigates the factorization of finite lattices to implode selected intervals while preserving remaining order structure. We examine how complete congruence relations and tolerance can be utilized for this purpose answer question finding finest those a given interval in generated factor lattice. To overcome limitations based on relations, we introduce new lattice that enables implod...

in this paper, we consider an arbitrary binary polynomial sequence {a_n} and then give a lower triangular matrix representation of this sequence. as main result, we obtain a factorization of the in nite generalized pascal matrix in terms of this new matrix, using a riordan group approach. further some interesting results and applications are derived.