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- W111910240 abstract "This chapter presents the theorems of Stein–Rosenberg type II. It discusses The paths of optimal relaxation, for small complex relaxation factors for the extrapolated Jacobi iterative method and for the successive overrelaxation iterative method. The spectral radii of the optimized extrapolated Jacobi matrix and optimized successive overrelaxation matrix have the same asymptotic expansions through first order terms in r as r → 0. It is observed that because of the crude estimation of perturbation effects, it is not possible to say which of these optimized procedures is faster as r → 0, unlike the classical Stein–Rosenberg theorem. It is found that if the Jordan normal form corresponding to some eigenvalue in the subset is not diagonal and if the perturbation with r > 0 small separates the eigenvalues associated with this Jordan block, then the optimized extrapolated, Jacobi method will be asymptotically faster than the optimized successive overrelaxation method for all r > 0 sufficiently small." @default.
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- W111910240 date "1981-01-01" @default.
- W111910240 modified "2023-09-25" @default.
- W111910240 title "THEOREMS OF STEIN-ROSENBERG TYPE II. OPTIMAL PATHS OF RELAXATION IN THE COMPLEX PLANE" @default.
- W111910240 cites W2001374433 @default.
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- W111910240 doi "https://doi.org/10.1016/b978-0-12-632620-8.50020-6" @default.
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