Abstract
The theory of linear, stationary, norm-reducing type iterations for the solution of linear, simultaneous equations is briefly reviewed and the genesis of simple iterition, Jacobi iteration and Gauss-Seidel iteration is shown to be the consequence of ‘splitting’ the coefficient matrix in different ways. For positive definite, sparse matrices arising in structural applications, block Gauss-Seidel iteration is shown to be effective for both reanalysis and initial analysis, through its influence as a norm-reducing aid which results in more pronounced ‘diagonal dominance’ and a better initial choice of starting vector. A numerical example is used to show the effectiveness of the method.
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