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This chapter presents a convergence theory for a fairly general two-level algorithm applied to a nonsymmetric operator with positive real part. The final convergence bounds are separated into a “smoothing property” and two separate “approximation properties”, one for the prolongation and one for the restriction, a novel feature of the theory, and one that depends critically on the absolute value presented in the previous chapter. Also shown is how, in the symmetric case, the theory reduces to reproduce and in some cases slightly generalize existing results from the literature.
KeywordsSymmetric Case Positive Real Part Ideal Weight Hierarchical Decomposition Prolongation Operator