We investigate several ways to improve the performance of sparse LU factorization with partial pivoting, as used to solve unsymmetric linear systems. We introduce the notion of unsymmetric supernodes to perform most of the numerical computation in dense matrix kernels. We introduce unsymmetric supernode-panel updates and two-dimensional data partitioning to better exploit the memory hierarchy. ...

The superscript H refers to the Hermitian transpose, which includes transposition and complex conjugation. That is, for any matrix A, AH = AT . An eigenvector of A, as defined above, is sometimes called a right eigenvector of A, to distinguish from a left eigenvector. It can be seen that if y is a left eigenvector of A with eigenvalue λ, then y is also a right eigenvector of AH , with eigenvalu...

A process for the gram scale synthesis of the oxygen bridged dimer of boron subphthalocyanine, μ-oxo-(BsubPc)2, has been developed. During the development it was found that a wide range of reaction pathways under diverse conditions lead to μ-oxo-(BsubPc)2 formation. However, obtaining μ-oxo-(BsubPc)2 as the main reaction product in appreciable yields and its subsequent isolation were extremely ...

The Eigen-FLS approach using an eigenspace-based scheme for fast fuzzy logic system (FLS) establishments has been attempted successfully in speech pattern recognition. However, speech pattern recognition by Eigen-FLS will still encounter a dissatisfactory recognition performance when the collected data for eigen value calculations of the FLS eigenspace is scarce. To tackle this issue, this pape...

A rhodium-catalysed stitching reaction between 2-(silylethynyl)arylboronates and 2-(silylethynyl)aryl bromides has been developed for the synthesis of unsymmetric dibenzo[a,e]pentalenes. The introduction of appropriately sized silyl groups on the starting substrates led to a high crossover selectivity without using an excess amount of either substrate. The present stitching reaction could produ...

Spectrum sensing is a fundamental component in cognitive radio. New sensing methods are proposed based on the principal component values of the received signal at the secondary users. In particular, two sensing algorithms are suggested, one of the algorithm is based on the ratio of the principal component’s maximum eigen value to principal component’s minimum eigen value called as Maximum Minim...