The linear equations that arise in interior methods for constrained optimization are sparse
symmetric indefinite, and they become extremely ill-conditioned as the interior method …

Linear solvers for reservoir simulation applications are the objective of this review.
Specifically, we focus on techniques for Fully Implicit (FI) solution methods, in which the set …

The generalized minimum residual method (GMRES) is a commonly used iterative Krylov
solver for sparse, non-symmetric systems of linear equations. Like other iterative solvers …

Generating sparsity patterns for effective block-Jacobi preconditioners is a challenging and
computationally expensive task, in particular for problems with unknown origin. In this paper …

Feedforward computation, such as evaluating a neural network or sampling from an
autoregressive model, is ubiquitous in machine learning. The sequential nature of …

While heterogeneous architectures are increasing popular with High Performance
Computing systems, their effectiveness depends on how efficient the scheduler is at …

The GMRES algorithm of Saad and Schultz [SIAM J. Sci. Stat. Comput., 7 (1986), pp. 856–
869] is an iterative method for approximately solving linear systems, with initial guess and …

The sparse triangular solve (SpTRSV) kernel is an important building block for a number of
linear algebra routines such as sparse direct and iterative solvers. The major challenge of …

Sparse linear iterative solvers are essential for many large-scale simulations. Much of the
runtime of these solvers is often spent in the implicit evaluation of matrix polynomials via a …

В работе предлагаются два способа применения MPI+ OpenMP технологии для
безытерационного построения и обращения предобусловливателя блочного Якоби в …