Determination of the D1/2-Norm of the SOR Iterative Matrix for the Unsymmetric Case
نویسندگان
چکیده
This paper is concerned with the determination of the Jordan canonical form and D1/,2-norm of the SOR iterative matrix derived from the coefficient matrix A having the form *-& t) with D\ and Di symmetric and positive definite. The theoretical results show that the Jordan form is not diagonal, but has only q principal vectors of grade 2 and that the D1//2-norm of J2?Ub (u^, the optimum parameter) is less than unity if and only if ß = p(B), the spectral radius of the associated Jacobi iterative matrix, is less than unity. Here q is the multiplicity of the eigenvalue iß of B.
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