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

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

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. vol. 76 (1954) pp. 92-111. MR**0059635 (15:562b)****[2]**S. Frankel,*Convergence rates of iterative treatments of partial differential equations*, Math. Tables and Other Aids to Computation vol. 4 (1950) pp. 65-75. MR**0046149 (13:692e)****[3]**D. W. Peaceman and H. H. Rachford, Jr.,*The numerical solution of parabolic and elliptic differential equations*, J. Soc. Indust. Appl. Math. vol. 3 (1955) pp. 28-41. MR**0071874 (17:196d)****[4]**J. 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. vol. 82 (1956) pp. 421-439. MR**0084194 (18:827f)****[5]**Gerard Debreu and I. N. Herstein,*Nonnegative square matrices*, Econometrica vol. 21 (1953) pp. 597-607. MR**0059240 (15:496f)****[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*, Proc. Amer. Math. Soc. vol. 8 (1957) pp. 409-411. MR**0090876 (19:884g)**

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

Article copyright:
© Copyright 1959
American Mathematical Society