Rubens Sampaio
Professor Titular,
Dept. de Engenharia Mecânica, PUC-Rio
On the Karhunen-Love basis for continuous
systems
Usually the Karhunen-Loeve basis is presented for Rn vectors. In
this framework, the KL basis is equivalent to the Principal Component
Analysis and to the Singular Value Decomposition. The proposal of
this paper is to show another point-of-view. We work in function
spaces and two different frameworks are presented to interpret the
KL process to obtain a basis. Both are Hilbert Spaces but the inner
products are different. We also address the following questions: how
to compute the KL basis, how to construct a reduce model of a given
dynamics using the basis, how to reproduce the dynamics, and what
is the relation between the KL basis and other concepts of modes.
