Implicit alternating direction methods

Authors:
Garrett Birkhoff and Richard S. Varga

Journal:
Trans. Amer. Math. Soc. **92** (1959), 13-24

MSC:
Primary 65.00; Secondary 35.00

MathSciNet review:
0105814

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References | Similar Articles | Additional Information

**[1]**David Young,*Iterative methods for solving partial difference equations of elliptic type*, Trans. Amer. Math. Soc.**76**(1954), 92–111. MR**0059635**, 10.1090/S0002-9947-1954-0059635-7**[2]**Stanley P. Frankel,*Convergence rates of iterative treatments of partial differential equations*, Math. Tables and Other Aids to Computation**4**(1950), 65–75. MR**0046149**, 10.1090/S0025-5718-1950-0046149-3**[3]**D. W. Peaceman and H. H. Rachford Jr.,*The numerical solution of parabolic and elliptic differential equations*, J. Soc. Indust. Appl. Math.**3**(1955), 28–41. MR**0071874****[4]**Jim Douglas Jr. and H. H. Rachford Jr.,*On the numerical solution of heat conduction problems in two and three space variables*, Trans. Amer. Math. Soc.**82**(1956), 421–439. MR**0084194**, 10.1090/S0002-9947-1956-0084194-4**[5]**Gerard Debreu and I. N. Herstein,*Nonnegative square matrices*, Econometrica**21**(1953), 597–607. MR**0059240****[6]**E. L. Wachspress,*CURE: A generalized multigroup coding for the IBM*-704, Report KAPL-1724 of the Knolls Atomic Power Laboratory, August, 1957.**[7]**G. Birkhoff and R. S. Varga,*Implicit alternating direction methods*, Report WAPD-T-650 of Westinghouse Electric Corp., October, 1957.**[8]**Jim Douglas Jr.,*A note on the alternating direction implicit method for the numerical solution of heat flow problems*, Proc. Amer. Math. Soc.**8**(1957), 409–412. MR**0090876**, 10.1090/S0002-9939-1957-0090876-7

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DOI:
https://doi.org/10.1090/S0002-9947-1959-0105814-4

Article copyright:
© Copyright 1959
American Mathematical Society