Block circular and hyperbolic transformations for the block fast array RLS algorithm

Both circular and hyperbolic transformations are needed in the scalar fast array RLS (FARLS) algorithm to transform the pre-array into the post-array. These transformations ‘compress’ (in a J-unitary sense) the energy of the first column of the pre-array into the first entry of the post-array. Analogous transformations are needed in the block FARLS (BFARLS) algorithm, except the transformations need to ‘compress’ the energy of certain block matrices of the pre-array into the first square block of the post-array. A stable J-unitary block reflector is developed in this paper for transforming the pre-array into the post-array for the BFARLS algorithm.

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