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On the convergence of line iterative methods for cyclically reduced non-symmetrizable linear systems (1994)

Elman, Howard C. ; Golub, Gene H. ; Starke, Gerhard

Springer

Numerische Mathematik 67 (1994), S. 177-190

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ISSN: 0945-3245

Keywords: Mathematics Subject Classification (1991): 65F10

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Summary. We derive analytic bounds on the convergence factors associated with block relaxation methods for solving the discrete two-dimensional convection-diffusion equation. The analysis applies to the reduced systems derived when one step of block Gaussian elimination is performed on red-black ordered two-cyclic discretizations. We consider the case where centered finite difference discretization is used and one cell Reynolds number is less than one in absolute value and the other is greater than one. It is shown that line ordered relaxation exhibits very fast rates of convergence.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s002110050023

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