We report on an extensive experiment to compare an iterative solver preconditioned by several versions of incomplete LU factorization with a sparse direct solver using LU factorization with partial pivoting. Our test suite is 24 nonsymmetric matrices drawn from benchmark sets in the literature. On a few matrices, the best iterative method is more than 5 times as fast and more than 10 times as m...

We report on an extensive experiment to compare an iterative solver preconditioned by several versions of incomplete LU factorization with a sparse direct solver using LU factorization with partial pivoting. Our test suite is 24 nonsymmetric matrices drawn from benchmark sets in the literature. On a few matrices, the best iterative method is more than 5 times as fast and more than 10 times as m...

Many computer graphics applications boil down to solving sparse systems of linear equations. While the current arsenal numerical solvers available in various specialized libraries and for different architectures often allow efficient scalable solutions image processing, modeling simulation applications, an increasing number problems face large-scale ill-conditioned --- a challenge which typical...

Consider the solution of a sparse linear system Ax = b when the matrix A is symmetric and positive definite. A typical iterative solver is obtained by using the method of Conjugate Gradients (CG) [15] preconditioned with an incomplete Cholesky (IC) factor L̂ [4]. The latter is an approximation to the (complete) Cholesky factor L, where A = LL . Consequently, the process of computing L̂ relies to ...

In this talk I will introduce a preconditioner based on low-rank compression of Schur complements. The construction is inspired by the well-known nested dissection strategy, and relies on the assumption that the Schur complements that arise in the elimination process can be approximated, to high precision, by compressible matrices. The preconditioner is built as an approximate LDM t factorizati...

We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CP-rank tensor capturing the global information and a sparse tensor capturing the local information (also considered as outliers), thus providing the robust predictive distribution over missing entries. The lowCP-rank tensor is ...

In this paper we present a new incomplete factorization of a square matrix into triangular factors in which we get standard LU or LDL T factors (direct factors) and their inverses (inverse factors) at the same time. Algorithmically, we derive this method from the approach based on the Sherman-Morrison formula [18]. In contrast to the RIF algorithm [11], the direct and inverse factors here direc...

This research investigates the implementation mechanism of block-wise ILU(k) preconditioner on GPU. The block-wise ILU(k) algorithm requires both the level k and the block size to be designed as variables. A decoupled ILU(k) algorithm consists of a symbolic phase and a factorization phase. In the symbolic phase, a ILU(k) nonzero pattern is established from the point-wise structure extracted fro...