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 Lanczos algorithm is becoming accepted as a powerful tool for finding the eigenvalues and for solving linear systems of equations. Any practical implementation of the algorithm suffers however from roundoff errors, which usually cause the Lanczos vectors to lose their mutual orthogonality. In order to maintain some level of orthogonality, full reorthogonalization (FRO) and selective orthogo...

The symmetric band Lanczos process is an extension of the classical Lanczos algorithm for symmetric matrices and single starting vectors to multiple starting vectors. After n iterations, the symmetric band Lanczos process has generated an n× n projection, Tn, of the given symmetric matrix onto the n-dimensional subspace spanned by the first n Lanczos vectors. This subspace is closely related to...

The Riemann-Lanczos problem for 4-dimensional manifolds was discussed by Bampi and Caviglia. Using exterior differential systems they showed that it was not an involutory differential system until a suitable prolongation was made. Here, we introduce the alternative Janet-Riquier theory and use it to consider the Riemann-Lanczos problem in 2 and 3 dimensions. We find that in 2 dimensions, the Ri...

In a semiorthogonal Lanczos algorithm, the orthogonality of the Lanczos vectors is allowed to deteriorate to roughly the square root of the rounding unit, after which the current vectors are reorthogonalized. A theorem of Simon 4] shows that the Rayleigh quotient | i.e., the tridiagonal matrix produced by the Lanczos recursion | contains fully accurate approximations to the Ritz values in spite...

This paper describes a parallel implementation of a generalized Lanczos procedure for structural dynamic analysis on a distributed memory parallel computer. One major cost of the generalized Lanczos procedure is the factorization of the (shifted) stiffness matrix and the forward and backward solution of triangular systems. In this paper, we discuss load assignment of a sparse matrix and propose...

We analyze the Lanczos method for matrix function approximation (Lanczos-FA), an iterative algorithm computing $f(\mathbf{A}) \mathbf{b}$ when $\mathbf{A}$ is a Hermitian and $\mathbf{b}$ given vector. Assuming that $f : \mathbb{C} \rightarrow \mathbb{C}$ piecewise analytic, we give framework, based on Cauchy integral formula, which can be used to derive priori posteriori error bounds Lanczos-F...

The Lanczos method is often used to solve a large and sparse symmetric matrix eigenvalue problem. It is well-known that the single-vector Lanczos method can only find one copy of any multiple eigenvalue. To compute all or some of the copies of a multiple eigenvalue, one has to use the block Lanczos method which is also known to compute clustered eigenvalues much faster than the single-vector La...