SLIDING WINDOW ADAPTIVE FAST QR AND QR-LATTICE ALGORITHMS

Sliding window formulations of the fast QR and fast QR-lattice algorit hms are presented. The derivations are based on the partial triangular ization of raw data matrices. Three methods for window downdating are discussed: the method of plane hyperbolic rotations, the Chambers' met hod, and the LINPACK algorithm. A numerically ill-conditioned stationa ry signal and a speech signal are used in finite wordlength simulation s of the full QR (nonfast), fast QR, and QR-lattice algorithms. All al gorithms are observed to be numerically stable over billions of iterat ions for double-precision mantissas (53 bits), but as the number of bi ts is decreased in the mantissa, the algorithms exhibit divergent beha vior, Hence, practically, the algorithms can be regarded as numericall y stable for long wordlengths.