Low Rank Approximation by Ivan Markovsky

Author:Ivan Markovsky
Language: eng
Format: epub
Publisher: Springer London, London

4.2 Model Reduction

Approximate Realization

Define the 2-norm ∥ΔH∥2 of a matrix-valued signal ΔH∈(ℝ p×m ) T+1 as

and let σ be the shift operator

Acting on a finite time series (H(0),H(1),…,H(T)), σ removes the first sample H(0).

Problem 4.1

(Approximate realization)

Given H d∈(ℝ p×m ) T and a complexity specification l, find an optimal approximate model for H d of a bounded complexity (m,l), such that

Problem 4.1 is equivalent to Problem SLRA, with norm ∥⋅∥=∥⋅∥2,

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