Sheldon and modified sheldon methods for matrices with red-black ordering

Abstract

We investigate the sheldon method [1] and Modified Sheldon method [2] for the linear system Ax = b, where A has the form,

with D ₁ and D ₂ symmetric and positive definite. We obtain explicit expressions for the spectral radii and the D ^1/2-norms of the iterative matrices of the two methods. The theoretical results show that we can not get any benefit by using the two methods compared with the optimum SOR, according to either the spectral radii or the D ^1/2-norms.

Keywords:

• Sheldon method
• Modified Sheldon method
• SOR method
• Modified SOR method
• spectral radius
• D ^1/2-norm

C.R. Categories:

• G.1.3

^*Corresponding author.

^*Corresponding author.

Notes

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Additional information

Notes on contributors

D.J. Evans

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