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Fast algorithms for finite shift-rank processes: A geometric approach. (English) Zbl 0538.65019
Outils et modèles mathématiques pour l’automatique, l’analyse de systèmes et le traitement du signal, Vol. 2, Trav. Rech. Coop. Programme 567, 499-527 (1982).
Summary: [For the entire collection see Zbl 0533.00040.]
Various algorithms acting on the covariances of processes with finite shift-rank-fast Cholesky decomposition, fast inverse triangular decomposition (or extended Levinson) and fast inversion via doubling - are shown to be direct applications of some general update formulas. The derivation of these formulas involves the introduction of two random vectors, the ”gap” variables, associated with any finite shift-rank process, and, a systematic use of simple arguments from linear least- squares estimation.

MSC:
65F30 Other matrix algorithms (MSC2010)
65F05 Direct numerical methods for linear systems and matrix inversion
65F20 Numerical solutions to overdetermined systems, pseudoinverses