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On the computation of the structured total least squares estimator

By I. Markovsky, S. Van Huffel and A. Kukush


A class of structured total least squares problems is considered, in which the extended data matrix is partitioned into blocks and each of the blocks is (block) Toeplitz/Hankel structured, unstructured, or noise free. We describe the implementation of two types of numerical solution methods for this problem: i) standard local optimization methods in combination with efficient evaluation of the cost function and its gradient, and ii) an iterative procedure proposed originally for the element-wise weighted total least squares problem. The computational efficiency of the proposed methods is compared with this of alternative methods. Application of the structured total least squares problem for system identification and model reduction is described and illustrated with numerical examples

Year: 2004
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Provided by: e-Prints Soton
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  1. (1999). 499–539. Copyright ?
  2. (1965). A simplex method for function minimization. doi
  3. (2002). About the convergence of the computational algorithm for the EW-TLS estimator.
  4. (1963). An algorithm for least squares estimation of non-linear parameters. doi
  5. (1980). An analysis of the total least squares problem. doi
  6. (2002). Consistency of the structured total least squares estimator in a multivariate model. doi
  7. (1964). Estimation of a system pulse transfer function in the presence of noise. doi
  8. (2000). Fast algorithm for solving the Hankel=Toeplitz structured total least squares problem. Numerical Algorithms doi
  9. (2001). Fast and reliable algorithms for structured total least squares and related matrix problems. doi
  10. (2000). Fast structured total least squares algorithm for solving the basic deconvolution problem. doi
  11. (1996). Formulation and solution of structured total least norm problems for parameter estimation. doi
  12. (1994). L2-optimal linear system identi cation structured total least squares for SISO systems. doi
  13. (1970). On a priori error estimates of some identi cation methods. doi
  14. (1970). On certain convergence questions in system identi cation. doi
  15. (2002). On the computation of the structured total least squares estimator. doi
  16. (1999). Practical Optimization.
  17. (1982). S oderstr om T. Bias correction in least-squares identi cation.
  18. SLICOT—a subroutine library in systems and control theory. doi
  19. (1993). Structured total least squares and L2 approximation problems. Linear Algebra and Its Applications doi
  20. (1999). Structured total least squares: analysis, algorithms and applications. doi
  21. (1991). The constrained total least squares technique and its application to harmonic superresolution. doi
  22. (2002). The element-wise weighted total least squares problem. doi
  23. (2002). The parametric quadratic form method for solving tls problems with elementwise weighting. In Total Least Squares and Errors-in-Variables Modeling: Analysis, Algorithms and Applications, Van Hu el S, Lemmerling P (eds). doi
  24. (1991). The Total Least Squares Problem: Computational Aspects and Analysis. doi
  25. (1996). Total least norm formulation and solution of structured problems. doi
  26. (1994). Total least squares for a nely structured matrices and the noisy realization problem. doi

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