Computer Analysis of Large-Scale Systems.
HAWAII UNIV HONOLULU DEPT OF ELECTRICAL ENGINEERING
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Solutions of large, sparse systems of equations need, as a rule, some preprocessing of the equations to minimize round-off errors, increase overall speed of computation and conserve memory space. Two existing major preprocessing methods are those of Kron strong tearing and Steward weak tearing. Krons method involves removal of matrix elements to reduce it to a block diagonal form and Stewards method reduces the matrix to a block triangular form by removal of one or more elements. In this dissertation the author presents a new algorithm for optimal weak tearing of large, sparse systems. Next, by working on the directed graph associated with the matrix A, the author develops a computer procedure which rapidly partitions the torn matrix into its constituent triangular blocks. Finally, rather than use an iterative method with its attendant poor convergence properties to obtain the solution of the original system the author derives a method of modified solutions. This enables the final solution to be obtained from the solution of the simple block triangular system by a very simple step. Author
- Theoretical Mathematics
- Computer Programming and Software