### Monday, July 14

8:30 AM-9:15 AM

*Chair: Gene H. Golub, Stanford University*

*Kresge Auditorium*

## IP1

Structured Total Least Squares, the Riemannian SVD and Applications in Signal Processing and System Identification

The least squares approximation of a given matrix by a rank deficient one can be obtained from its singular value decomposition (SVD). However, in general, this procedure does not preserve the structure, if any, in the data matrix (such as e.g. Hankel, Toeplitz, etc..).

Yet the combination of structure and rank deficiency is crucial in many applications, ranging from biomedical signal processing, over telecommunications, to system identification for model-based process
control.

In this presentation, the speaker will discuss a nonlinear generalization of the SVD, called the Riemannian SVD, which delivers a rank deficient least squares approximation of a given data matrix, while preserving its (affine) structure. He will discuss geometrical, algebraic, and statistical properties and interpretations and numerical issues. Several practical engineering examples will be illustrated.

**Bart De Moor**

*ESAT/SISTA, Katholieke Universiteit Leuven, Belgium*

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*MMD, 3/26/97*
*tjf, 5/27/97*