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The recursive least squares (RLS) algorithm is well known and has been widely used for many years. Most analyses of RLS have assumed statistical properties of the data or the noise process, but recent robust ℌ∞ analyses have been used to bound the ratio of the performance of the algorithm to the total noise. In this paper, we provide an additive analysis bounding the difference between performance and noise. Our analysis provides additional convergence guarantees in general, and particular benefits for structured input data. We illustrate the analysis using human speech and white noise.