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Medientyp:
E-Artikel
Titel:
Gaussian elimination
Beteiligte:
Higham, Nicholas J.
Erschienen:
Wiley, 2011
Erschienen in:WIREs Computational Statistics
Sprache:
Englisch
DOI:
10.1002/wics.164
ISSN:
1939-5108;
1939-0068
Entstehung:
Anmerkungen:
Beschreibung:
<jats:title>Abstract</jats:title><jats:p>As the standard method for solving systems of linear equations, Gaussian elimination (GE) is one of the most important and ubiquitous numerical algorithms. However, its successful use relies on understanding its numerical stability properties and how to organize its computations for efficient execution on modern computers. We give an overview of GE, ranging from theory to computation. We explain why GE computes an LU factorization and the various benefits of this matrix factorization viewpoint. Pivoting strategies for ensuring numerical stability are described. Special properties of GE for certain classes of structured matrices are summarized. How to implement GE in a way that efficiently exploits the hierarchical memories of modern computers is discussed. We also describe block LU factorization, corresponding to the use of pivot blocks instead of pivot elements, and explain how iterative refinement can be used to improve a solution computed by GE. Other topics are GE for sparse matrices and the role GE plays in the TOP500 ranking of the world's fastest computers. <jats:italic>WIREs Comp Stat</jats:italic> 2011 3 230–238 DOI: 10.1002/wics.164</jats:p><jats:p>This article is categorized under:
<jats:list list-type="explicit-label">
<jats:list-item><jats:p>Applications of Computational Statistics > Computational Mathematics</jats:p></jats:list-item>
<jats:list-item><jats:p>Algorithms and Computational Methods > Numerical Finite Arithmetic</jats:p></jats:list-item>
<jats:list-item><jats:p>Algorithms and Computational Methods > Numerical Methods</jats:p></jats:list-item>
</jats:list></jats:p>