Task-parallel tiled direct solver for dense symmetric indefinite systems

A Dense Complex Symmetric Indefinite Solver for the Fujitsu AP3000

Solving dense symmetric indefinite systems using GPUs

This paper studies the performance of different algorithms for solving a dense symmetric indefinite linear system of equations on multicore CPUs with a Graphics Processing Unit (GPU). To ensure the numerical stability of the factorization, pivoting is required. Obtaining high performance of such algorithms on the GPU is difficult because all the existing pivoting strategies lead to frequent syn...

Symmetric Indefinite Linear Solver using OpenMP Task on Multicore Architectures

Recently, the Open Multi-Processing (OpenMP) standard has incorporated task-based programming, where a function call with input and output data is treated as a task. At run time, OpenMP’s superscalar scheduler tracks the data dependencies among the tasks and executes the tasks as their dependencies are resolved. On a shared-memory architecture with multiple cores, the independent tasks are exec...

A Parallel Distributed Solver for Large Dense Symmetric Systems: Applications to Geodesy and Electromagnetism Problems

In this paper we describe the parallel distributed implementation of a linear solver for large-scale applications involving real symmetric positive definite or complex symmetric non-Hermitian dense systems. The advantage of this routine is that it performs a Cholesky factorization by requiring half the storage needed by the standard parallel libraries ScaLAPACK and PLAPACK. Our solver uses a Jv...

An Efficient and Stable Method for Parallel Factorization of Dense Symmetric Indefinite Matrices

This paper investigates the efficient parallelization of algorithms with strong stability guarantees to factor dense symmetric indefinite matrices. It shows how the bounded Bunch-Kaufman algorithm may be efficiently parallelized, and then how its performance can be enhanced by using exhaustive block searching techniques, which is effective in keeping most symmetric interchanges within the curre...