We present algorithms for the symbolic and numerical factorization phases in the direct solution of sparse unsymmetric systems of linear equations. We have modified a classical symbolic factorization algorithm for unsymmetric matrices to inexpensively compute minimal elimination structures. We give an efficient algorithm to compute a near-minimal data-dependency graph for unsymmetric multifront...

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...

PIRO BAND is a library for bidiagonal reduction of unsymmetric banded matrices and tridiagonal reduction of symmetric banded matrices. It supports both real and complex matrices stored in packed band format. The software also can handle single and double precision arithmetic with 32-bit and 64-bit integers. We provide both a C library and MATLAB callable interfaces. The library is about 2 to 7 ...

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...