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Iterative speed improvement for solving slowly varying total least squares problems. (English) Zbl 0669.93068

Many problems in signal processing, modal analysis, system identification, etc., give rise to an overdetermined set of linear equations AX\(\approx B\). Whenever both the observation matrix B and the data matrix A are inaccurate, the total least squares (TLS) method is appropriate for estimating the unknown parameters X. Since the TLS solution is deduced from only one right singular vector or, in general, a basis of the right singular subspace associated with the smallest singular values of the data [A;B], the computational speed can be improved by only calculating those desired base vectors. If a priori information is available (e.g. the TLS solution at a previous time step when slowly varying sets of equations must be solved at each time instant), iterative methods are appropriate to compute those base vectors. It is shown in this paper that inverse iteration is the most efficient iterative technique for solving generic TLS problems of known rank.
Two algorithms for subspace inverse iteration are presented. Their convergence properties and applicability in solving TLS problems are analysed. Based on the convergence rate and the operation counts in each iteration step, these iterative algorithms are compared in efficiency with the direct computation methods - classical TLS and partial TLS. In particular, the efficiency of these methods is illustrated in a practical real life problem, namely multiple input estimation of frequency response functions.

MSC:

93E10 Estimation and detection in stochastic control theory
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
93E25 Computational methods in stochastic control (MSC2010)
93E12 Identification in stochastic control theory
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