Abstract
This chapter is devoted to applying the analysis developed in the previous chapter to the iterative solution of systems of linear equations. In particular, we will discuss in detail the Jacobi and the Gauss-Seidel iterations, which essentially go back to Gauss. InSupplementum Theoriae Combinationis Observationum Erroribus Minime Obnoxiapublished in 1822, Gauss used a variant of the Gauss-Seidel method for the solution of the linear systems arising through his least squares method, since they were too large for elimination methods.
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© 1998 Springer Science+Business Media New York
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Kress, R. (1998). Iterative Methods for Linear Systems. In: Numerical Analysis. Graduate Texts in Mathematics, vol 181. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0599-9_4
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DOI: https://doi.org/10.1007/978-1-4612-0599-9_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6833-8
Online ISBN: 978-1-4612-0599-9
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