The fast recursive row-Householder subspace tracking algorithm

We introduce a new sequential algorithm for tracking the principal subspace and, optionally, the rr dominant eigenvalues and associated eigenvectors of an exponentially updated covariance matrix of dimension N×NN×N, where N>rN>r. 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 3Nr3Nr 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.