Erin Carson

TL;DR: The results suggest that on architectures for which half precision is efficiently implemented it will be possible to solve certain linear systems up to twice as fast and to greater accuracy, as well as recommending a standard solver that uses LU factorization in single precision.

TL;DR: This paper describes lower bounds on communication in linear algebra, and presents lower bounds for Strassen-like algorithms, and for iterative methods, in particular Krylov subspace methods applied to sparse matrices.

TL;DR: A GMRES-based iterative refinement method that makes use of the computed LU factors as preconditioners and can succeed where standard refinement fails, and that it can provide accurate solutions to systems with condition numbers of order $u^{-1}$ and greater.

TL;DR: A number of theoretical results and algorithmic techniques developed for classical Krylov subspace methods are extended to communication-avoiding KrylovSubspace methods and constraints under which these methods are competitive in terms of both achieving asymptotic speedups and meeting application-specific numerical requirements are identified.

TL;DR: This work provides a comprehensive survey of mixed-precision numerical linear algebra routines, including the underlying concepts, theoretical background, and experimental results for both dense and sparse linear algebra problems.