Communication lower bounds and optimal algorithms for numerical linear algebra

G Ballard, E Carson, J Demmel, M Hoemmen… - Acta Numerica, 2014 - cambridge.org
The traditional metric for the efficiency of a numerical algorithm has been the number of
arithmetic operations it performs. Technological trends have long been reducing the time to …

[BOG][B] Avoiding communication in dense linear algebra

GM Ballard - 2013 - search.proquest.com
Dense linear algebra computations are essential to nearly every problem in scientific
computing and to countless other fields. Most matrix computations enjoy a high …

Communication-avoiding parallel algorithms for solving triangular systems of linear equations

T Wicky, E Solomonik, T Hoefler - 2017 IEEE International …, 2017 - ieeexplore.ieee.org
We present a new parallel algorithm for solving triangular systems with multiple right hand
sides (TRSM). TRSM is used extensively in numerical linear algebra computations, both to …

[PDF][PDF] Parallel numerical algorithms

MT Heath - Lecture Notes, 2011 - relate.cs.illinois.edu
Computation speed is limited by physical laws Speed of conventional processors is limited
by line delays: signal transmission time between gates gate delays: settling time before state …

Communication-Avoiding Parallel Algorithms for Solving Triangular Matrix Equations

T Wicky - 2015 - research-collection.ethz.ch
In this work an algorithm for solving triangular systems of equations for multiple right hand
sides is presented. The algorithm for solving triangular systems for multiple right hand sides …