Research Article
Jul 1973
Solution of Linear Equations—State-of-the-Art
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VIEW THE REPLYPublication: Journal of the Structural Division
Volume 99, Issue 7
Abstract
Most problems in structural analysis require at some stage the solution of linear equations which may require considerable execution times even on today's computers. This paper is a state-of-the-art review of research efforts directed towards computer algorithms to solve large equation systems accurately and economically. Many different solution techniques are analyzed, with emphasis on the physical interpretation of the various strategies. First, the standard Gauss algorithm is reviewed, followed by a consideration of modifications due to symmetry, the Cholesky algorithm, and a physical interpretation of the reduction process. Particular attention is given to specialized direct solution techniques of more recent data, such as various band solutions, partitioning methods (static condensation, substructuring), and frontal solutions. A short summary of iterative methods concludes this paper.
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Published In
Journal of the Structural Division
Volume 99 • Issue 7 • July 1973
Pages: 1507 - 1526
Copyright
© 1973 American Society of Civil Engineers.
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Published in print: Jul 1973
Published online: Feb 1, 2021
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Authors
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Christian Meyer, AM.ASCE
Sr. Systems Engr., Albert C. Martin and Assocs., Los Angeles, CA
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Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.