The LU factorization is an important numerical algorithm for solving systems of linear equations in science and engineering, and is characteristic of many dense linear algebra computations. It has even become the de facto numerical algorithm implemented within the LINPACK benchmark to rank the most powerful supercomputers in the world, collected bt the TOP500 website. In this context, the chall...

Steady state simulations in Computational Fluid Dynamics (CFD), which rely on implicit time integration, are not experiencing great accelerations on GPUs. Moreover, most of the reported acceleration effort concerns solving the linear system of equations while neglecting the acceleration potential of running the entire simulation on the GPU. In this paper, we present the software implementation ...

Matrix factorization (or often called decomposition) is a frequently used kernel in a large number of applications ranging from linear solvers to data clustering and machine learning. The central contribution of this paper is a thorough performance study of four popular matrix factorization techniques, namely, LU, Cholesky, QR, and SVD on the STI Cell broadband engine. The paper explores algori...

A Class of Splitting Preconditioners for the iterative solution of Linear Systems arising from Interior Point Methods for Linear Programming Problems needs to find a base by a sophisticated process based in a lying rectangular LU factorization, that involves reordering columns many times until certain conditions are satisfied. At the same time, it is necessary to prevent excessive fill-in in L ...

A novel algorithm for computing the incomplete-LU and Cholesky factorization with 0 fill-in on a graphics processing unit (GPU) is proposed. It implements the incomplete factorization of the given matrix in two phases. First, the symbolic analysis phase builds a dependency graph based on the matrix sparsity pattern and groups the independent rows into levels. Second, the numerical factorization...

Decomposing a matrix $\mathbf {A}$ into lower {L}$ and an upper {U}$ , which is also known as LU decomposition, essential operation in numerical linear algebra. For sparse matrix, decomposition often introduces more nonzero entries the factors than original matrix. A <i...

and Applied Analysis 3 linear systems with the same matrix of coefficients, by using LU factorization, is