Improved convergence criteria for Jacobi and Gauss-Seidel iterations

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2004

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Elsevier Science inc

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Some simple criteria for the convergence of the Jacobi, Gauss-Seidel and SOR iterations have been proposed in the work of Huang [ZAMM 76-1 (1996) 57-58]. In this study we present some modified forms of the criteria introduced in Huang's work. The new criteria also allow for the norms of the Jacobi iteration matrices to be greater than unity. Numerical examples are also given which show the effectiveness of the criteria. (C) 2003 Elsevier Inc. All rights reserved.

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iterative methods, spectral radius, convergence

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Volume

152

Issue

3

Start Page

693

End Page

700

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https://doi.org/10.1016/S0096-3003(03)00587-3
 https://hdl.handle.net/20.500.14411/1091

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