The Minimal Residual (MR) is modified for adaptive
filtering application. Three forms of MR based algorithm are
presented: i) the low complexity SPCG, ii) MREDSI, and iii)
MREDSII. The low complexity is a reduced complexity version of a
previously proposed SPCG algorithm. Approximations introduced
reduce the algorithm to an LMS type algorithm, but, maintain the
superior convergence of the SPCG algorithm. Both MREDSI and
MREDSII are MR based methods with Euclidean direction of search.
The choice of Euclidean directions is shown via simulation to give
better misadjustment compared to their gradient search counterparts.
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