Transformation for Solving Linear Equations

by Robert J. Melosh, (M.ASCE), Vice Pres.; MARC Analysis Research Corp., Palo Alto, Calif., and Virginia Polytechnic and State Univ., Blacksburg, Va.,

Serial Information: Journal of the Structural Division, 1977, Vol. 103, Issue 6, Pg. 1289-1302

Document Type: Journal Paper


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.

Subject Headings: Computing in civil engineering | Gaussian process | Decomposition | Hybrid methods | Linear functions | Finite element method | Algorithms | Permits

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