Updating the principal angle decomposition

Abstract

A class of fast Householder-based sequential algorithms for updating the Principal Angle Decomposition is introduced. The updated Principal Angle Decomposition is of key importance in the adaptive implementation of several fundamental operations on correlated processes, such as adaptive Wiener filtering, rank-adaptive system identification, and rank and data compression concepts using canonical coordinates. An instructive example of rank-adaptive system identification is examined experimentally. Mathematics Subject Classification (2000)15A18 · 15A23 · 15A29 · 65F05 · 65F15 · 65F20

Square-root Householder subspace tracking

“…The use of a square-root subspace tracker is not only motivated by numerical and dynamic range considerations. Sometimes, the power matrix square-root is even a conceptual prerequisite, for instance, in the area of low-rank tracking of principal angle decompositions and canonical coordinates [17].…”