We present our work on the sparse Cholesky factorization using a hypermatrix data structure. First, we provide some background on the sparse Cholesky factorization and explain the hypermatrix data structure. Next, we present the matrix test suite used. Afterwards, we present the techniques we have developed in pursuit of performance improvements for the sparse hypermatrix Cholesky factorization...

A new preconditioner for symmetric positive definite systems is proposed, analyzed, and tested. The preconditioner, compressed incomplete modified Gram–Schmidt (CIMGS), is based on an incomplete orthogonal factorization. CIMGS is robust both theoretically and empirically, existing (in exact arithmetic) for any full rank matrix. Numerically it is more robust than an incomplete Cholesky factoriza...

In 1961 Youla published his paper 'On the factorization of rational matrices'. He proved that any proper rational parahermitian matrix, positive definite on the imaginary axis can be factorized as the product of a proper rational matrix, stable with respect to the closed right half plane, and its adjoint. In this paper I prove that for any positive definite, nonstrictly proper matrix this facto...

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 ( ...

The WZ factorization for the solution of symmetric positive definite banded linear systems when combined with a partitioned scheme, renders a divide and conquer algorithm. The WZ factorization of the coefficient matrix in each block has the properties: the vector [a1, . . . , aβ , 0, . . . , 0, an−β+1, . . . , an] is invariant under the transformation W where β is the semibandwidth of the coeff...

In this paper, a procedure is reported that discuss how linear algebra can be used in image compression. The basic idea is that each image can be represented as a matrix. We apply linear algebra (QR ‎factorization and wavelet ‎transformation ‎algorithm‏s) on this matrix and get a reduced matrix out such that the image corresponding to this reduced matrix requires much less storage space than th...

using qcd factorization for the hadronic matrix elements, we show that existing data, inparticular the branching ratios br ( b →j/ψk) and br ( b →j/ψπ), can be accounted for in this approach.we analyze the decay b j /k( ) within the framework of qcd factorization. the calculation of therelevant hard-scattering kernels for twist-2 and twist-3 is completed. we calculate this decay in a special...