Abstract
A classical result on linear asynchronous iterations states that convergence occurs if and only if the spectral radius of the modulus matrix is less than 1. The present paper shows that if one introduces very mild restrictions on the admissible asynchronous processes, one gets convergence for a larger class of matrices for which the spectral radius of the modulus matrix is allowed to be equal to 1. The mild restrictions are virtually always fulfilled in practical implementations. In this manner, our result contributes to the better understanding of the different hypotheses underlying mathematical models for asynchronous iterations.
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Frommer, A., Spiteri, P. (2001). On Linear Asynchronous Iterations when the Spectral Radius of the Modulus Matrix is One. In: Alefeld, G., Chen, X. (eds) Topics in Numerical Analysis. Computing Supplementa, vol 15. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6217-0_8
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DOI: https://doi.org/10.1007/978-3-7091-6217-0_8
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