Estimating optimum overrelaxation parameters

Authors:
L. A. Hageman and R. B. Kellogg

Journal:
Math. Comp. **22** (1968), 60-68

MSC:
Primary 65.35

DOI:
https://doi.org/10.1090/S0025-5718-1968-0229371-6

MathSciNet review:
0229371

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References | Similar Articles | Additional Information

**[1]**G. E. Forsythe & W. R. Wasow,*Finite-Difference Methods for Partial Differential Equations*, Wiley, New York, 1960. MR**23**#B3156. MR**0130124 (23:B3156)****[2]**R. S. Varga,*Matrix Iterative Analysis*, Prentice-Hall, Englewood Cliffs, N. J., 1962. MR**28**#1725. MR**0158502 (28:1725)****[3]**B. A. Carre, "The determination of the optimum accelerating factor for successive overrelaxation,"*Comput. J.*, v. 4, 1961, pp. 73-78.**[4]**H. E. Kulsrud, "A practical technique for the determination of the optimum relaxation factor of the successive over-relaxation method,"*Comm. ACM*, v. 4, 1961, pp. 184-187. MR**26**#895. MR**0143336 (26:895)****[5]**A. K. Rigler, "Estimation of the successive over-relaxation factor,"*Math. Comp.*, v. 19, 1965, pp. 302-307. MR**31**#5351. MR**0181122 (31:5351)****[6]**E. L. Wachspress,*Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics*, Prentice-Hall, Englewood Cliffs, N. J., 1966. MR**0234649 (38:2965)****[7]**G. H. Golub & R. S. Varga, "Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods. I, II,"*Numer. Math.*, v. 3, 1961, pp. 147-156, 157-168. MR**26**#3207; MR**26**#3208.**[8]**D. A. Flanders & G. Shortley, "Numerical determination of fundamental modes,"*J. Appl. Phys.*, v. 21, 1950, pp. 1326-1332. MR**0040075 (12:640b)****[9]**L. A. Hageman,*The Chebyshev Polynomial Method of Iteration*, WAPD-TM-537, 1967. (Available from the Clearinghouse for Federal Scientific and Technical Information, National Bureau of Standards, U. S. Department of Commerce, Springfield, Virginia.)**[10]**R. S. Varga,*Numerical Methods for Solving Multi-Dimensional Multigroup Diffusion Equations*, Proc. Sympos. Appl. Math., Vol. 11, Amer. Math. Soc., Providence, R. I., 1961, pp. 164-189. MR**23**#B595. MR**0127549 (23:B595)****[11]**G. J. Tee, "Eigenvectors of the successive overrelaxation process, and its combination with Chebyshev semi-iteration,"*Comput. J.*, v. 6, 1963, pp. 250-263.**[12]**J. K. Reid, "A method for finding the optimum successive overrelaxation parameter,"*Comput. J.*, v. 9, 1966, pp. 200-204. MR**33**#3475. MR**0195273 (33:3475)****[13]**L. A. Hageman & R. B. Kellogg.*Estimating Optimum Acceleration Parameters for Use in the Successive Overrelaxation and the Chebyshev Polynomial Methods of Iteration*, WAPD-TM-592, 1966. (Available from the Clearinghouse for Federal Scientific and Technical Information; see reference 9.)

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DOI:
https://doi.org/10.1090/S0025-5718-1968-0229371-6

Article copyright:
© Copyright 1968
American Mathematical Society