Abstract
In this chapter we consider the general properties of iterative methods. Such properties are consistency, ensuring the connection between the iterative method and the given system of equations, as well as convergence, guaranteeing the success of the iteration. The most important result of this chapter is the characterisation of the convergence of linear iterations by the spectral radius of the iteration matrix (cf. §3.1.3). Since we consider iterative methods for systems with regular matrices only, iterative methods for singular systems or those with rectangular matrices will not be studied. Concerning this topic, we refer to Maess [2], Marek [1], and Kosmol-Zhou [1].
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© 1994 Springer-Verlag New York, Inc.
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Hackbusch, W. (1994). Iterative Methods. In: Iterative Solution of Large Sparse Systems of Equations. Applied Mathematical Sciences, vol 95. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4288-8_3
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DOI: https://doi.org/10.1007/978-1-4612-4288-8_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8724-7
Online ISBN: 978-1-4612-4288-8
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