There is a growing need for the ability to specify and generate correlated random variables as primitive inputs to stochastic models. Motivated by this need, several authors have explored the generation of random vectors with speciied marginals, together with a speciied covariance matrix, through the use of a transformation of a multivariate normal random vector. A covariance matrix is said to ...

In this paper we generalize the framework of linear loop transformations in the sense that loop alignment is considered as a new component in the transformation process. The aim is to match the structure of loop nests with the data distribution and alignment in order to eliminate non-local references whenever possible when compiling a sequential program for a distributed memory machine. The ali...

Using the method of the block matrix construction and generalized elementary transformation given in the paper, readers can easily prove the inequalities of rank of matrix on skew field. Mathematics Subject Classification: 05A19; 15A15

In this paper, we research the run-time sparse matrix data transformation from Compressed Row Storage (CRS) to Coordinate (COO) storage and an ELL (ELLPACK/ITPACK) format with OpenMP parallelization for sparse matrix-vector multiplication (SpMV). We propose an auto-tuning (AT) method by using the Dmat i Rell graph, which plots the derivation/average for the number of non-zero elements per row (...

The Metropolis-Hastings algorithm transforms a given stochastic matrix into a reversible stochastic matrix with a prescribed stationary distribution. We show that this transformation gives the minimum distance solution in an L1 metric.

This paper treats data reduction in array processing for the spatially colored noise case. The purpose is to reduce the computational complexity of the applied signal processing algorithms by mapping the data into a space of lower dimension by means of a linear transformation. We discuss ways to implement the transformation and show that it suffices to estimate the array covariance matrix inste...

Elastic matrix distortion around a growing inclusion of a new phase is analyzed and the associated contribution to the Gibbs free energy is considered. The constant-composition transformation from the parent to product phase is considered within the frame of Landau theory of phase transitions. The volume misfit between the inclusion and matrix is assumed to originate from the transformation vol...

We study the modular transformation of Zn-symmetric elliptic R-matrix and construct the twist between the trigonometric degeneracy of the elliptic R-matrix. Mathematics Subject Classifications (1991): 17B37, 81R10, 81R50, 16W30.

We determine the number of functionally independent components of tensors involving higher–order derivatives of a Riemannian metric. A central problem in Riemannian geometry is to determine the number of functionally independent invariants which can be constructed out from a Riemannian metric and its derivatives up to a given order. Due to the inmediate applications of these invariants as Lagra...