The fast recursive row-Householder subspace tracking algorithm

  • Authors:
  • Peter Strobach

  • Affiliations:
  • AST-Consulting Inc., Bahnsteig 6, 94133 Röhrnbach, Germany

  • Venue:
  • Signal Processing
  • Year:
  • 2009

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Abstract

We introduce a new sequential algorithm for tracking the principal subspace and, optionally, the r dominant eigenvalues and associated eigenvectors of an exponentially updated covariance matrix of dimension NxN, where Nr. The method is based on an updated orthonormal-square (QS) decomposition using the row-Householder reduction. This new subspace tracker reaches a dominant complexity of only 3Nr multiplications per time update for tracking the principal subspace, which is the lower bound in dominant complexity for an algorithm of this kind. The new method is completely reflection based. An updating of inverse matrices is not used.