By L. Auslander, R. Tolimieri

ISBN-10: 3540071342

ISBN-13: 9783540071341

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This is exploited via the Schur algorithm. 2.

In particular, their convergence properties are well understood, while the convergence properties of the RiSVD, MLPCA, and PR methods are still not. 5. Misfit Minimization* 45 In order to apply a classical optimization algorithm for the solution of (WTLS), first we have to choose a parameterization of the model. Possible parameterizations are given by the kernel, image, and input/output representations. 26), we choose the input/output representation (I/Orepr), defined on page 34, so that the considered problem is (WTLSx).

For example, they can be selected by noise variance estimation from repeated measurements or from prior knowledge about the accuracy of the measurement devices. 2. Kernel, Image, and Input/Output Representations A practical application of the WTLS problem occurs in chemometrics, where the aim is to estimate the concentrations of certain chemical substances in a mixture from spectral measurements on the mixture. For details see [Wao97, SMWV05]. 2 Kernel, Image, and Input/Output Representations In this section we review three common representations of a linear static model: kernel, image, and input/output.

### Abelian Harmonic Analysis Theta Functions and Function Algebras on a Nilmanifold by L. Auslander, R. Tolimieri

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