By Sabine Van Huffel

ISBN-10: 9048159571

ISBN-13: 9789048159574

ISBN-10: 9401735522

ISBN-13: 9789401735520

In reaction to a growing to be curiosity in overall Least Squares (TLS) and Errors-In-Variables (EIV) modeling through researchers and practitioners, famous specialists from a number of disciplines have been invited to arrange an outline paper and current it on the 3rd overseas workshop on TLS and EIV modeling held in Leuven, Belgium, August 27-29, 2001. those invited papers, representing two-thirds of the ebook, including a variety of alternative awarded contributions yield an entire evaluation of the most medical achievements because 1996 in TLS and Errors-In-Variables modeling. during this method, the ebook well completes previous books on TLS (SIAM 1991 and 1997). not just computational concerns, but in addition statistical, numerical, algebraic houses are defined, in addition to many new generalizations and purposes. Being conscious of the becoming curiosity in those ideas, it's a powerful trust that this publication will reduction and stimulate clients to use the recent strategies and types adequately to their very own useful problems.

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In this phase, the Lanczos vector qi is orthogonalized against previously generated Lanczos vectors ql, . ,qi-l, hence it requires complete reorthogonalization. This is not a serious drawback for the application we have in mind because k « min( m, n) and m + n - 1 = 2P for some small whole number p, usually 8 ::; p ::; 10. The Lanczos algorithm runs a fixed number max_iter of steps, say max_iter = k or 2k, and then the residuals are computed to identify the converged Ritz values AI, ... , Akl and Ritz vectors VI, ...

47 S. Van Huffel and P. ), Total Least Squares and Errors·in-Variables Modeling, 47-56. © 2002 Kluwer Academic Publishers. 48 1. D. C. Hansen Introduction The singular value decomposition (SVD) of a data matrix is useful for providing rank and subspace information as well as solving and analyzing total least squares (TLS) problems. This orthogonal decomposition is an important analytical tool and the algorithm is highly regarded, but for many applications the SVD requires too much storage, computation time, or cannot be implemented efficiently for situations that involve adding new data or deleting old data.

Acknowledgments The authors are grateful to Leentje Vanhamme and Sabine Van Huffel at the Dept. U. (Leuven, Belgium) for helpful discussions concerning the BioSource Database [23]. Rank-revealing and Lanczos methods for solving TLS-related problems 55 References [1] H. Barkhuijsen, R. D. Beer, and D. V. Ormondt. Improved Algorithm for Noniterative Time-Domain Model Fitting to Exponentially Damped Magnetic Resonance Signals. J. Magn. , 30:553-557, 1987. [2] J. L. Barlow, P. A. Yoon, and H. Zhao An Algorithm and a Stability Theory for Downdating the ULV Decomposition.

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Total Least Squares and Errors-in-Variables Modeling: Analysis, Algorithms and Applications by Sabine Van Huffel

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