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]**George E. Forsythe and Wolfgang R. Wasow,*Finite-difference methods for partial differential equations*, Applied Mathematics Series, John Wiley & Sons, Inc., New York-London, 1960. MR**0130124****[2]**Richard S. Varga,*Matrix iterative analysis*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR**0158502****[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**4**(1961), 184–187. MR**0143336**, https://doi.org/10.1145/355578.366504**[5]**A. K. Rigler,*Estimation of the successive over-relaxation factor*, Math. Comp.**19**(1965), 302–307. MR**0181122**, https://doi.org/10.1090/S0025-5718-1965-0181122-7**[6]**Eugene L. Wachspress,*Iterative solution of elliptic systems, and applications to the neutron diffusion equations of reactor physics*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1966. MR**0234649****[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]**Donald A. Flanders and George Shortley,*Numerical determination of fundamental modes*, J. Appl. Phys.**21**(1950), 1326–1332. MR**0040075****[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]**Richard S. Varga,*Numerical methods for solving multi-dimensional multi-group diffusion equations*, Proc. Sympos. Appl. Math., Vol. XI, American Mathematical Society, Providence, R.I., 1961, pp. 164–189. MR**0127549****[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 over-relaxation parameter*, Comput. J.**9**(1966), 200–204. MR**0195273**, https://doi.org/10.1093/comjnl/9.2.200**[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