Detail publikace

Pivoting Strategy for Fast LU decomposition of Sparse Block Matrices

POLOK, L. SMRŽ, P.

Originální název

Pivoting Strategy for Fast LU decomposition of Sparse Block Matrices

Typ

článek ve sborníku ve WoS nebo Scopus

Jazyk

angličtina

Originální abstrakt

Solving large linear systems is a fundamental task in many interesting problems, including finite element methods (FEM) or (non-)linear least squares (NLS), among others. Furthermore, the problems of interest here are sparse: not all the vertices in a typical FEM mesh are connected, or similarly not all vertices in a graphical inference model are linked by observations, as is the case in e.g. simultaneous localization and mapping (SLAM) in robotics or bundle adjustment (BA) in computer vision. The two places where most of the time is spent in solving such problems are usually the sparse matrix assembly and solving the underlying linearized system. An interesting property of the above-mentioned problems is their block structure. It is given by the variables existing in a multi-dimensional space such as 2D, 3D or even se(3) and hence their respective derivatives being dense blocks of the corresponding dimension. In our previous work, we demonstrated the benefits of explicitly representing those blocks in the sparse matrix, namely reduced assembly time and increased efficiency of arithmetic operations. In this paper, we propose a novel implementation of sparse block LU decomposition and demonstrate its benefits on standard datasets. While not difficult to implement, the enabling feature is the pivoting strategy that makes the method numerically stable. The proposed algorithm is on average three times faster (over 50x faster in the best case), causes less fill-in and produces decompositions of comparable and often better precision than the conventional methods.

Klíčová slova

LU decomposition, sparse matrix, block matrix, register blocking, direct methods.

Autoři

POLOK, L.; SMRŽ, P.

Vydáno

23. 4. 2017

Nakladatel

Association for Computing Machinery

Místo

Virginia Beach, VA

ISBN

978-1-5108-3822-2

Kniha

Proceedings of the 25th High Performance Computing Symposium

Strany od

1

Strany do

12

Strany počet

12

URL

BibTex

@inproceedings{BUT134093,
  author="Lukáš {Polok} and Pavel {Smrž}",
  title="Pivoting Strategy for Fast LU decomposition of Sparse Block Matrices",
  booktitle="Proceedings of the 25th High Performance Computing Symposium",
  year="2017",
  pages="1--12",
  publisher="Association for Computing Machinery",
  address="Virginia Beach, VA",
  doi="10.22360/SpringSim.2017.HPC.049",
  isbn="978-1-5108-3822-2",
  url="https://doi.org/10.22360/SpringSim.2017.HPC.049"
}