American Society of Civil Engineers

Solution of Linear Equations—State-of-the-Art

by Christian Meyer, A.M.ASCE, (Sr. Systems Engr., Albert C. Martin and Assocs., Los Angeles, CA)

Journal of the Structural Division
, Vol. 99, No. 7, July 1973, pp. 1507-1526

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Document type: Journal Paper
Discussion: by Anil K. Kar    (See full record)
Discussion: by Frederic W. Williams    (See full record)
Discussion: by Th. Lunde Johnsen and et al.    (See full record)
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.

ASCE Subject Headings:
Differential equations
Linear analysis
Matrices (mathematics)
Numerical analysis