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Mathematics of Computation

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Matrix representations of nonlinear equation iterations--Application to parallel computation


Author: John R. Rice
Journal: Math. Comp. 25 (1971), 639-647
MSC: Primary 65H05
DOI: https://doi.org/10.1090/S0025-5718-1971-0303714-7
MathSciNet review: 0303714
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Abstract: A matrix representation of iterative methods is presented which includes almost all those based on polynomial methods. A simple lemma and corollaries are established which show that the order of convergence of the iteration is the spectral radius of the matrix representation. A number of old and new methods, particularly those adapted to parallel computation, are analyzed using this representation.


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DOI: https://doi.org/10.1090/S0025-5718-1971-0303714-7
Keywords: Nonlinear equations, parallel computation, iteration, matrix representations, convergence order
Article copyright: © Copyright 1971 American Mathematical Society