Pivoting Strategy for Fast LU decomposition of Sparse Block Matrices

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26230%2F17%3APU123021" target="_blank" >RIV/00216305:26230/17:PU123021 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.22360/SpringSim.2017.HPC.049" target="_blank" >https://doi.org/10.22360/SpringSim.2017.HPC.049</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.22360/SpringSim.2017.HPC.049" target="_blank" >10.22360/SpringSim.2017.HPC.049</a>

Result language

angličtina

Original language name

Pivoting Strategy for Fast LU decomposition of Sparse Block Matrices

Original language description

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.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2017

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Proceedings of the 25th High Performance Computing Symposium

ISBN

978-1-5108-3822-2

ISSN

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e-ISSN

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Number of pages

12

Pages from-to

1-12

Publisher name

Association for Computing Machinery

Place of publication

Virginia Beach, VA

Event location

Virginia Beach, VA

Event date

Apr 23, 2017

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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