A Modified Conjugate Gradient scheme to solve sparse linear systems with positive definite coefficient matrices has been implemented on a microcomputer. A discussion of its mathematical properties shows that it is a good algorithm for small computers. The representation of the data used in the implementation requires the storage only of the non zero elements of the coefficient matrix, thus attaining a great saving of memory space. Test examples are given for matrices arising from the finite element analysis of structural problems, and the performance of the Conjugate Gradient scheme is compared with that of other algorithms commonly used to solve sparse linear systems on microcomputers.
A Modified Conjugate Gradient Method for the Solution of Sparse Linear Systems on Microcomputers
SARTORETTO, Flavio
1984-01-01
Abstract
A Modified Conjugate Gradient scheme to solve sparse linear systems with positive definite coefficient matrices has been implemented on a microcomputer. A discussion of its mathematical properties shows that it is a good algorithm for small computers. The representation of the data used in the implementation requires the storage only of the non zero elements of the coefficient matrix, thus attaining a great saving of memory space. Test examples are given for matrices arising from the finite element analysis of structural problems, and the performance of the Conjugate Gradient scheme is compared with that of other algorithms commonly used to solve sparse linear systems on microcomputers.
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