hal-02947991
https://inria.hal.science/hal-02947991
https://inria.hal.science/hal-02947991v1/document
https://inria.hal.science/hal-02947991v1/file/qr_with_tournament_pivoting.pdf
Communication avoiding low rank approximation based on QR with tournament pivoting
BeaupĂ¨re, Matthias
Grigori, Laura
[INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation
[INFO.INFO-NA] Computer Science [cs]/Numerical Analysis [cs.NA]
UNDEFINED
QR decomposition
Communication avoiding algorithm
Subset selection
Low rank approximation
We introduce a parallel algorithm for computing the low rank approximation $A_k$ of a large matrix $A$ which minimizes the number of messages exchanged between processors (modulo polylogarithmic factors) and has guarantees for the approximations of the singular values of $A$ provided by $A_k$. This operation is essential in many applications in scientific computing and data analysis when dealing with large data sets. Our algorithm is based on QR factorization that consists in selecting a subset of columns from the matrix $A$ that allow to approximate the range of $A$, and then projecting the columns of $A$ on a basis of the subspace spanned by those columns. The selection of columns is performed by using tournament pivoting, a strategy introduced previously for matrices partitioned into blocks of columns. This strategy is extended here to matrices partitioned along both dimensions that are distributed on a two-dimensional grid of processors, and also to tournaments with more general reduction trees. Performance results show that the algorithm scales well on up to $1024$ cores of $16$ nodes.
2020-09-24
2020-09-24
en