Numerical linear algebra algorithms and software

Numerical Linear Algebra Algorithms and Software

Numerical linear algebra software

at the current iterate x ∈ Rn. In practice, we find that the bulk of computational resources (memory, time) consumed by these algorithms is spent constructing and solving these linear systems, and not in the higher-level algorithmic details. That is not to say that the higher-level details do not impact performance; for example, algorithmic improvements could result in a reduction in the number...

Standardized Numerical Linear Algebra Software

Randomized algorithms in numerical linear algebra

This survey provides an introduction to the use of randomization in the design of fast algorithms for numerical linear algebra. These algorithms typically examine only a subset of the input to solve basic problems approximately, including matrix multiplication, regression and low-rank approximation. The survey describes the key ideas and gives complete proofs of the main results in the field. A...

Communication lower bounds and optimal algorithms for numerical linear algebra

Acta Numerica / Volume 23 / May 2014, pp 1 155 DOI: 10.1017/S0962492914000038, Published online: 12 May 2014 Link to this article: http://journals.cambridge.org/abstract_S0962492914000038 How to cite this article: G. Ballard, E. Carson, J. Demmel, M. Hoemmen, N. Knight and O. Schwartz (2014). Communication lower bounds and optimal algorithms for numerical linear algebra . Acta Numerica, 23, pp ...