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Preconditioning strategies for elliptic partial differential operators and corresponding difference operators are compared by way of a model problem. The technique considered here makes use of a selfadjoint positive definite operator B as the preconditioner for the nonselfadjoint convection -diffusion operator A. Preconditioning by A’s leading term plus a positive zeroth-order term σ I and optimizing over σ is proposed. The analysis of a model problem indicates that when A has large first-order terms, both the spectral and norm condition of B- 1 A are minimized by σ 0.
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Manteuffel et al. (1993) studied this question.
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