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On the effects of scaling of the Peaceman-Rachford method


Author: Olof B. Widlund
Journal: Math. Comp. 25 (1971), 33-41
MSC: Primary 65N10
DOI: https://doi.org/10.1090/S0025-5718-1971-0303754-8
MathSciNet review: 0303754
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Abstract: The alternating direction method of Peaceman and Rachford is considered for elliptic difference schemes of second order and with two independent variables. An earlier result of the author's on the rapid convergence of multi-parameter noncommutative problems is described and a connection is established between that result and theorems on optimal scaling of band matrices. Simple algorithms to decrease the condition number and increase the rate of convergence are discussed.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1971-0303754-8
Keywords: Alternating direction implicit methods, Peaceman-Rachford method, elliptic of second order, multi-parameter, noncommutative, separation-of-variables, condition number, rate of convergence, optimal scaling
Article copyright: © Copyright 1971 American Mathematical Society