In this paper we describe an Incomplete LU factorization technique based on a strategy which combines two heuristics. This ILUT factorization extends the usual ILU(0) factorization without using the concept of level of ll-in. There are two traditional ways of developing incomplete factorization preconditioners. The rst uses a symbolic factorization approach in which a level of ll is attributed ...

We give a review of the theory of factorization of block Toeplitz matrices of the type T = (Ti−j)i,j∈Zd , where Ti−j are complex k × k matrices, in the form T = LDU, with L and L−1 lower block triangular, U and U−1 upper block triangular Toeplitz matrices, and D a diagonal matrix function. In particular, it is discussed how decay properties of Ti a ect decay properties of L, L−1, U , and U−1. W...

In this paper we analyze the Gauss-Huard algorithm. From a description of the algorithm in terms of matrix-vector operations we reveal a close relation between the Gauss-Huard algorithm and an LU factorization as constructed in an ikj variant.

Lower/Upper triangular (LU) factorization plays an important role in scientific and high performance computing. This paper presents an implementation of the LU decomposition algorithm for double precision complex numbers on a star topology based multi-FPGA platform. The out of core implementation moves data through multiple levels of a hierarchical memory system (hard disk, DDR SDRAMs and FPGA ...

Bipartite graphs are used to describe the generalized Schur complements of real matrices having no square submatrix with two or more nonzero diagonals. For any matrix A with this property, including any nearly reducible matrix, the sign pattern of each generalized Schur complement is shown to be determined uniquely by the sign pattern of A. Moreover, if A has a normalized LU factorization A = L...