Abstract
In Chap. 1, the equivalence between line fitting and rank-one matrix approximation was considered. This chapter extends the equivalence to general linear static and dynamic linear time-invariant data modeling problems. First, three linear static model representations—kernel, image, and input/output—are defined and the connections among them are shown. Then, representations of linear time-invariant dynamic models are defined. Finally, exact and approximate modeling problems are related to low rank approximation problems. In the general case of linear dynamic modeling, the problem is Hankel structured low rank approximation.
… whenever we have two different representations of the same thing we can learn a great deal by comparing representations and translating descriptions from one representation into the other. Shifting descriptions back and forth between representations can often lead to insights that are not inherent in either of the representations alone.
Abelson and diSessa (1986, p. 105)
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Markovsky, I. (2012). From Data to Models. In: Low Rank Approximation. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-2227-2_2
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DOI: https://doi.org/10.1007/978-1-4471-2227-2_2
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