Premium
Almost block diagonal linear systems: sequential and parallel solution techniques, and applications
Author(s) -
Amodio P.,
Cash J. R.,
Roussos G.,
Wright R. W.,
Fairweather G.,
Gladwell I.,
Kraut G. L.,
Paprzycki M.
Publication year - 2000
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/1099-1506(200007/08)7:5<275::aid-nla198>3.0.co;2-g
Subject(s) - diagonal , mathematics , ordinary differential equation , boundary value problem , block (permutation group theory) , linear system , variety (cybernetics) , iterative method , computer science , algorithm , differential equation , mathematical analysis , geometry , statistics
Almost block diagonal (ABD) linear systems arise in a variety of contexts, specifically in numerical methods for two‐point boundary value problems for ordinary differential equations and in related partial differential equation problems. The stable, efficient sequential solution of ABDs has received much attention over the last fifteen years and the parallel solution more recently. We survey the fields of application with emphasis on how ABDs and bordered ABDs (BABDs) arise. We outline most known direct solution techniques, both sequential and parallel, and discuss the comparative efficiency of the parallel methods. Finally, we examine parallel iterative methods for solving BABD systems. Copyright © 2000 John Wiley & Sons, Ltd.