Several representations of the generalized Drazin inverse of an anti-triangular block matrix in Banach algebra are given in terms of the generalized Banachiewicz--Schur form.  

CSDP is a software package that implements the XZ primal–dual interior point method for semidefinite programming. In this method there are a number of computationally intensive steps including the construction of the Schur complement matrix O, the factorization of O, multiplications and Cholesky factorizations of matrices of size n. Profiling shows that for different problems, each of these typ...

We consider a linear-quadratic elliptic control problem (LQECP). For the problem 8 we consider here, the control variable corresponds to the Neumann data on the boundary of 9 a convex polygonal domain. The optimal control unknown is the one for which the harmonic 10 extension approximates best a specified target in the interior of the domain. We propose a 11 multilevel preconditioner for the re...

Abstract. In this paper we consider the solution of Hermitian positive definite block-Toeplitz systems with small size blocks. We propose and study block diagonal and Schur complement preconditioners for such block-Toeplitz matrices. We show that for some block-Toeplitz matrices, the spectra of the preconditioned matrices are uniformly bounded except for a fixed number of outliers and this fixe...

This paper introduces a new sweeping preconditioner for the iterative solution of the variable coefficient Helmholtz equation in two and three dimensions. The algorithms follow the general structure of constructing an approximate LDLt factorization by eliminating the unknowns layer by layer starting from an absorbing layer or boundary condition. The central idea of this paper is to approximate ...

The definitions of θ-ray pattern matrix and θ-ray matrix are firstly proposed to establish some new results on nonsingularity/singularity and convergence of general H-matrices. Then some conditions on the matrix A ∈ Cn×n and nonempty α ⊂ 〈n〉 = {1, 2, . . . , n} are proposed such that A is an invertible H-matrix if A(α) and A/α are both invertible H-matrices. Furthermore, the important results o...