MATRIX MANIPULATION BY COMPUTER: THE GENERAL SOLUTION OF LINEAR ALGEBRAIC EQUATIONS.
SYSTEM DEVELOPMENT CORP SANTA MONICA CALIF
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A computer program is described that gives the solution of a general set of M algebraic equations in N unknowns. The program reduces the given augmented matrix to an upper triangular array of K equations a check for consistency is then made of the remaining M-K equations. Consistent sets are solved for the unique solution vector if it exists or for dependencies of the unknowns. The order of retention or elimination of the variables may be specified. At the first pass the Gauss elimination process is used to arrive at the dependencies in the unknowns optionally the problem can be recycled to be recalculated using the now known dependencies by means of the method of pivotal condensation. The solution thus obtained may be further refined by iteration two options are provided simple iteration and Gauss -Seidel iteration. The program is arranged to provide copious intermediate printing, which can be selected either from control cards or from the computer console. The program represents an intermediate result in a sequence of programs developed to teach matrix manipulations by computer. The given version is not optimal in any sense, but was checked with a number of examples and found to perform satisfactorily. A FORTRAN II version for the Philco S-2000 computer is given. Author
- Theoretical Mathematics
- Computer Programming and Software