By Stanislaw Saks

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1 summarizes the model parameterizations and optimization algorithms for the different methods. 5. 1. Model representations and optimization algorithms used in the methods of [DM93, Wao97, PR02, MMH03]. , ^ = col span(P), where P e E dxm . First, we rewrite (WTLS) in the form The constraint D e <% is equivalent to D = PL, where L e RmxN, so that (WTLS) can further be written as The two problems derived from (WTLSp) by fixing, respectively, L and P to given values, are WLS problems and therefore can be solved in closed form.

1 Introduction In this chapter, we consider approximate modeling by the linear static model. /, and the model class is ^ = Jz^f0. The parameter m specifies the maximum allowed complexity for the approximating model. The matrix D := \d\ • • • d^ is called the data matrix. We use the shorthand notation The WTLS misfit between the data 3> and a model & e J^fo is defined as follows: where W^, . . , WN are given positive definite matrices. 29 30 Chapter 3. 1 (WTLS). 2 (Element-wise weighted total least squares) The special case when all weight matrices are diagonal is called element-wise weighted total least squares (EWTLS).

1 Introduction In this chapter, we consider approximate modeling by the linear static model. /, and the model class is ^ = Jz^f0. The parameter m specifies the maximum allowed complexity for the approximating model. The matrix D := \d\ • • • d^ is called the data matrix. We use the shorthand notation The WTLS misfit between the data 3> and a model & e J^fo is defined as follows: where W^, . . , WN are given positive definite matrices. 29 30 Chapter 3. 1 (WTLS). 2 (Element-wise weighted total least squares) The special case when all weight matrices are diagonal is called element-wise weighted total least squares (EWTLS).