206 citations · 535 across the 22 of their papers we have counts for
8 papers · 1 filter
Proposed Consistent Exception Handling for the BLAS and LAPACK
James Demmel, Jack Dongarra, Mark Gates +7
Numerical exceptions, which may be caused by overflow, operations like division by 0 or sqrt(-1), or convergence failures, are unavoidable in many cases, in particular when softwar…
A Survey of Numerical Methods Utilizing Mixed Precision Arithmetic
Ahmad Abdelfattah, Hartwig Anzt, Erik G. Boman +22
Within the past years, hardware vendors have started designing low precision special function units in response to the demand of the Machine Learning community and their demand for…
Bidiagonalization with Parallel Tiled Algorithms
Mathieu Faverge, Julien Langou, Yves Robert +1
We consider algorithms for going from a "full" matrix to a condensed "band bidiagonal" form using orthogonal transformations. We use the framework of "algorithms by tiles". Within…
Standards for Graph Algorithm Primitives
Tim Mattson, David Bader, Jon Berry +16
It is our view that the state of the art in constructing a large collection of graph algorithms in terms of linear algebraic operations is mature enough to support the emergence of…
Towards an Efficient Tile Matrix Inversion of Symmetric Positive Definite Matrices on Multicore Architectures
Emmanuel Agullo, Henricus Bouwmeester, Jack Dongarra +3
The algorithms in the current sequential numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multicore architectures. A new family of algorithms, the tile a…
Rectangular Full Packed Format for Cholesky's Algorithm: Factorization, Solution and Inversion
Fred G. Gustavson, Jerzy Wasniewski, Jack J. Dongarra +1
We describe a new data format for storing triangular, symmetric, and Hermitian matrices called RFPF (Rectangular Full Packed Format). The standard two dimensional arrays of Fortran…
Accelerating Scientific Computations with Mixed Precision Algorithms
Marc Baboulin, Alfredo Buttari, Jack Dongarra +5
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit f…
A Class of Parallel Tiled Linear Algebra Algorithms for Multicore Architectures
Alfredo Buttari, Julien Langou, Jakub Kurzak +1
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in or…