Determination of the -norm of the SOR iterative matrix for the unsymmetric case

Authors:
D. J. Evans and C. Li

Journal:
Math. Comp. **53** (1989), 203-218

MSC:
Primary 65F10; Secondary 65N99

DOI:
https://doi.org/10.1090/S0025-5718-1989-0969486-1

MathSciNet review:
969486

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the determination of the Jordan canonical form and -norm of the SOR iterative matrix derived from the coefficient matrix *A* having the form

*q*principal vectors of grade 2 and that the -norm of ( , the optimum parameter) is less than unity if and only if , the spectral radius of the associated Jacobi iterative matrix, is less than unity. Here

*q*is the multiplicity of the eigenvalue of

*B*.

**[1]**L. W. Ehrlich, "Coupled harmonic equations, SOR and Chebyshev acceleration,"*Math. Comp.*, v. 26, 1972, pp. 335-343. MR**0311128 (46:10224)****[2]**E. D. Nering,*Linear Algebra and Matrix Theory*, 2nd ed., Wiley, New York, 1970.**[3]**H. Späth, "The numerical calculation of high degree Lidstone splines with equidistant knots by block and overrelaxation,"*Computing*, v. 7, 1971, pp. 65-74. MR**0319348 (47:7892)****[4]**H. Späth,*Spline Algorithms for Curves and Surfaces*, Utilitas Math. Publishing Inc., Winnipeg, 1974. MR**0359267 (50:11722)****[5]**R. S. Varga,*Matrix Iterative Analysis*, Prentice-Hall, Englewood Cliffs, N.J., 1962. MR**0158502 (28:1725)****[6]**D. M. Young, "Iterative methods for solving partial differential equations of elliptic type,"*Trans. Amer. Math. Soc.*, v. 76, 1954, pp. 92-111. MR**0059635 (15:562b)****[7]**D. M. Young,*Iterative Solution of Large Linear Systems*, Academic Press, New York and London, 1971. MR**0305568 (46:4698)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1989-0969486-1

Keywords:
SOR iterative matrix,
-norm,
spectral radius,
spectral norm and Jordan canonical form

Article copyright:
© Copyright 1989
American Mathematical Society