In this paper we investigate a method to improve the performance of sparse LU matrix factorization used to solve unsymmetric linear systems, which appear in many mathematical models. We introduced and used the concept of the supernode for unsymmetric matrices in order to use dense matrix operations to perform the LU factorization for sparse matrices. We describe an algorithm that uses supernode...

Z. Naturforsch. 58b, 211 – 216 (2003); received Oktober 4, 2002 The oxidative coupling of various symmetric (5 7) as well as unsymmetric silicon bisnaphtholates (11, 12), initiated by different oxidants (iron(III), cerium(IV), copper(II) or hypervalent iodine), furnishes the corresponding symmetric and unsymmetric binaphthols 13 17. The coupling reaction of the substrates follows strictly an in...

A well-known approach to compute the LU factorization of a general unsymmetric matrix A is to build the elimination tree associated with the pattern of the symmetric matrix A + A and use it as a computational graph to drive the numerical factorization. This approach, although very eÆcient on a large range of unsymmetric matrices, does not capture the unsymmetric structure of the matrices. We in...

An efficient palladium-catalyzed cross-coupling reaction of azides with isocyanides is developed, providing a general synthetic route to unsymmetric carbodiimides with excellent yields. This method shows a broad substrate scope, including not only aryl azides, but also unactivated benzyl and alkyl azides. Furthermore, from readily available substrates, Pd-catalyzed coupling with a tandem amine ...

The first one-pot selective synthesis of unsymmetric tertiary amines is reported by the amination of two types of alcohols with primary amines via the development of a simple CuAlOx-HT catalyst and enables the synthesis of unsymmetric amines in a wide variety of primary amines and alcohols.

An advanced non-linear cascading filter algorithm for the removal of high density salt and pepper noise from the digital images is proposed. The proposed method consists of two stages. The first stage Decision base Median Filter (DMF) acts as the preliminary noise removal algorithm. The second stage is either Modified Decision Base Partial Trimmed Global Mean Filter (MDBPTGMF) or Modified Decis...

This report presents an experimental comparison of NAG Fortran Library software for the solution of large sparse unsymmetric linear systems of algebraic equations Preconditioned RGMRES CGS and Bi CGSTAB methods to be introduced at Mark are compared against one another and against direct methods Test problems include discrete approximations to D elliptic partial di erential equations random valu...

Sparse matrix factorization algorithms are typically characterized by irregular memory access patterns that limit their performance on parallel-vector supercomputers. For symmetric problems, methods such as the multifrontal method replace irregular operations with dense matrix kernels. However, no e cient method based primarily on dense matrix kernels exists for matrices whose pattern is very u...

The biorthogonal Lanczos and the biconjugate gradient methods have been proposed as iterative methods to approximate the solution of nonsymmetric and indefinite linear systems. Sonneveld (1989) obtained the conjugate gradient squared by squaring the matrix polynomials of the biconjugate gradient method. Here we square the unsymmetric (or biorthogonal) Lanczos method for computing the eigenvalue...