Funding Information Russian Science Foundation, Grant/Award Number: 14-31-00024 Summary The paper studies numerical properties of LU and incomplete LU factorizations applied to the discrete linearized incompressible Navier–Stokes problem also known as the Oseen problem. A commonly used stabilized Petrov–Galerkin finite element method for the Oseen problem leads to the system of algebraic equati...

Lower upper (LU) factorization for sparse matrices is the most important computing step for circuit simulation problems. However, parallelizing LU factorization on the graphic processing units (GPUs) turns out to be a difficult problem due to intrinsic data dependence and irregular memory access, which diminish GPU computing power. In this paper, we propose a new sparse LU solver on GPUs for ci...

In this paper we present several improvements of widely used parallel LU factorization methods on sparse matrices. First we introduce the LU elimination forest and then we characterize the L, U factors in terms of their corresponding LU elimination forest. This characterization can be used as a compact storage scheme of the matrix as well as of the task dependence graph. To improve the use of B...

The LU factorization is an important numerical algorithm for solving systems of linear equations in science and engineering and is a characteristic of many dense linear algebra computations. For example, it has become the de facto numerical algorithm implemented within the LINPACK benchmark to rank the most powerful supercomputers in the world, collected by the TOP500 website. Multicore process...

Componentand normwise perturbation bounds for the block LU factorization and block LDL∗ factorization of Hermitian matrices are presented. We also obtain, as a consequence, perturbation bounds for the usual pointwise LU, LDL∗, and Cholesky factorizations. Some of these latter bounds are already known, but others improve previous results. All the bounds presented are easily proved by using serie...