Total least squares methods
نویسندگان
چکیده
1. the use of weighted norms as a measure of the data perturbation size, capturing prior knowledge about uncertainty in the data; 2. the addition of constraints on the perturbation to preserve the structure of the data matrix, motivated by structured data matrices occurring in signal and image processing, systems and control, and computer algebra; 3. the use of regularization in the problem formulation, aiming at stabilizing the solution by decreasing the effect because of intrinsic ill-conditioning of certain problems.
منابع مشابه
Bibliography on total least squares and related methods
The class of total least squares methods has been growing since the basic total least squares method was proposed by Golub and Van Loan in the 70’s. Efficient and robust computational algorithms were developed and properties of the resulting estimators were established in the errors-in-variables setting. At the same time the developed methods were applied in diverse areas, leading to broad lite...
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Iron is an essential element used as supplement in different dosage-forms. Different time and expenditure-consuming methods introduced for detection and determination of elemental ions such as atomic absorption. In this research, two different and routine methods containing ATR-IR and atomic absorption were applied to define the amount of iron in 198 samples containing different concentrations ...
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A careful comparison between the Principal Component Analysis (PCA) and the Hankel Total Least Squares (HTLS) based methods for estimating the resonances in sets of MR spectra is presented. After a description of the methods and their relationships , we compare their performance on simulated data sets of Magnetic Resonance Spec-troscopy (MRS) signals and discuss their advantages and limitations.
متن کاملPartial least squares- least squares- support vector machine modeling of ATR-IR as a spectrophotometric method for detection and determination of iron in pharmaceutical formulations
Iron is an essential element used as supplement in different dosage-forms. Different time and expenditure-consuming methods introduced for detection and determination of elemental ions such as atomic absorption. In this research, two different and routine methods containing ATR-IR and atomic absorption were applied to define the amount of iron in 198 samples containing different concentrations ...
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Minimum residual norm iterative methods for solving linear systems Ax = b can be viewed as, and are often implemented as, sequences of least squares problems involving Krylov subspaces of increasing dimensions. The minimum residual method (MINRES) [C. Paige and M. Saunders, SIAM J. Numer. Anal., 12 (1975), pp. 617–629] and generalized minimum residual method (GMRES) [Y. Saad and M. Schultz, SIA...
متن کاملOverview of total least-squares methods
We review the development and extensions of the classical total least squares method and describe algorithms for its generalization to weighted and structured approximation problems. In the generic case, the classical total least squares problem has a unique solution, which is given in analytic form in terms of the singular value decomposition of the data matrix. The weighted and structured tot...
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