Research Article
Jun 1977
Transformation for Solving Linear Equations
Publication: Journal of the Structural Division
Volume 103, Issue 6
Abstract
This paper proposes an equation solving adjunct for improving the optimality of computer solution of many (thousands of) sparsely-populated linear equations. The paper provides a formal and computer implementation description of the algorithm, illustrating solution steps, and comparing equation solving by the process with modified Gauss decomposition. While the process increases calculations over Gauss decomposition, it is expected to reduce computer costs by factors up to seven because of its superior data handling potential. It permits imposing linear constraints and making equilibrium checks to be an integral part of the equation solving process. In the finite element analysis, assembly of the system stiffness and evaluation of element generalized forces can also be integrated with the equation solution. When an N-step iterative method is used for solving the transformed equations, it forms with the adjunct a hybrid iterative method which requires about the same number of calculations as Gauss decomposition.
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Published In
Journal of the Structural Division
Volume 103 • Issue 6 • June 1977
Pages: 1289 - 1302
Copyright
© 1977 American Society of Civil Engineers.
History
Published in print: Jun 1977
Published online: Feb 1, 2021
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Authors
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Robert J. Melosh, M.ASCE
Chf. Scientist, MARC Analysis Research Corp., Palo Alto, Calif.
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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.