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 | References | Similar Articles | Additional Information

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

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