Abstract
Direct methods for solving linear systems, with their large number of operations proportional to n 3, have a tendancy to accumulate rounding errors so that for a not ideally conditioned system matrix A, the solution can become entirely useless. In contrast, iterative methods are unaffected by rounding errors to a large extent, because each approximate solution with its inherent computational error can easily be improved upon in the following iteration step. Iterative methods typically require around n 2 operations for each iteration step, but, unfortunately, they do not converge for all solvable systems.
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© 1996 Springer-Verlag Berlin Heidelberg
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Engeln-Müllges, G., Uhlig, F. (1996). Iterative Methods for Linear Systems. In: Numerical Algorithms with C. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61074-5_5
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DOI: https://doi.org/10.1007/978-3-642-61074-5_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64682-9
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