Journal Article10.1061/JSDEAG.0002493
Efficient Solutions for Linear Matrix Equations
H. Gordon Jensen,Gary A. Parks +1 more
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TL;DR: Gaussian elimination and subsequent back substitution is presented for its implementation to minimize the amount of central computer memory required; provide a more flexible means of manipulating large matrices; and dramatically reduce computer time.
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Abstract: The most efficient means of solving most systems of linear equations arising in structural analysis is by Gaussian elimination and subsequent back substitution. A method is presented for its implementation. Direct solutions are obtained with sparse matrix factors which preserve the operations of the Gaussian elimination for repeat solutions. The method together with techniques for its application are graphically described. Its use in many types of engineering problems requiring solutions to systems of linear equations will: (1) Minimize the amount of central computer memory required; (2) provide a more flexible means of manipulating large matrices; and (3) dramatically reduce computer time.
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Citations
Computational methods of linear algebra
D. K. Faddeev,V. N. Faddeeva +1 more
TL;DR: A survey of computational methods in linear algebra can be found in this article, where the authors discuss the means and methods of estimating the quality of numerical solution of computational problems, the generalized inverse of a matrix, the solution of systems with rectangular and poorly conditioned matrices, and more traditional questions such as algebraic eigenvalue problems and systems with a square matrix.
689
Hypermatrix solution of large sets of symmetric positive-definite linear equations
TL;DR: The hypermatrix Cholesky approach is presented, as implemented by the authors and their colleagues as a part of the ASKA structural analysis package, in order to reduce both the time spent in performing the arithmetical operations as well as the required number of data transfers between core and external storage.
52
Computer Implementation of the Finite-Element Procedure
Ernst Schrem
- 01 Jan 1973
TL;DR: This chapter aims at presenting fundamental concepts for the implementation of the finite-element method, with primary emphasis on static analysis based upon the displacement method.
36
Substructuring and equation system solutions in finite element analysis
H. Petersson,E. P. Popov +1 more
TL;DR: In this article, a generalized Gaussian elimination scheme is presented for the solution of systems of equations in substructuring, which may be very useful in solutions of mixed finite element models, equation systems with Lagrangian multipliers and moderately ill-conditioned problems.
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