A sliding window update for the basis matrix of the QR decomposition

Mahon, Mark; Sibul, Leon H.; Valenzuela, H.M.

doi:10.1109/78.215313

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A Prediction Of the Front Edge Of Sliding Window1

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Cited by 10 publications

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“…The updates of the backward prediction variables are obtained similarly. The first column of is rotated via an orthonormal matrix (12) where manifests an order increase in Then, is annihilated by a rotation pivoted on to obtain the updates (13) where (14a)…”

Section: A Prediction Of the Front Edge Of Sliding Windowmentioning

confidence: 99%

Sliding window adaptive fast QR and QR-lattice algorithms

Baykal

Constantinides

1998

IEEE Trans. Signal Process.

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Abstract-Sliding window formulations of the fast QR and fast QR-lattice algorithms are presented. The derivations are based on the partial triangularization of raw data matrices. Three methods for window downdating are discussed: the method of plane hyperbolic rotations, the Chambers' method, and the LINPACK algorithm. A numerically ill-conditioned stationary signal and a speech signal are used in finite wordlength simulations of the full QR (nonfast), fast QR, and QR-lattice algorithms. All algorithms are observed to be numerically stable over billions of iterations for double-precision mantissas (53 bits), but as the number of bits is decreased in the mantissa, the algorithms exhibit divergent behavior. Hence, practically, the algorithms can be regarded as numerically stable for long wordlengths.

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Section: A Prediction Of the Front Edge Of Sliding Windowmentioning

confidence: 99%