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

MathSciNet review:
969486

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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*.

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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