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The Parametric Quadratic Form Method for Solving TLS Problems with Elementwise Weighting

In: Total Least Squares and Errors-in-Variables Modeling

Author

Listed:
  • Amedeo Premoli

    (Politecnico di Milano, Dipartimento di Elettronica e Informazione)

  • Maria Luisa Rastello

    (Istituto Elettrotecnico Nazionale G. Ferraris)

Abstract

This paper considers the Total Least Squares (TLS) problem with Elementwise Weighting (EW), removing the assumption of identical variances of data and observation errors while preserving their statistical independence. To solve them we approximate the gradient of the weighted Frobenius norm of errors by the gradient of an ad hoc Parametric Quadratic Form and present a fast iterative algorithm, exhibiting quadratic convergence. Some numerical examples show the capabilities of this algorithm in solving EW-TLS problems.

Suggested Citation

  • Amedeo Premoli & Maria Luisa Rastello, 2002. "The Parametric Quadratic Form Method for Solving TLS Problems with Elementwise Weighting," Springer Books, in: Sabine Van Huffel & Philippe Lemmerling (ed.), Total Least Squares and Errors-in-Variables Modeling, pages 67-76, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-3552-0_7
    DOI: 10.1007/978-94-017-3552-0_7
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