Two algorithms for fast approximate subspace tracking

New fast algorithms are presented for tracking singular values, singular ve ctors, and the dimension of a signal subspace through an overlapping sequen ce of data matrices. The basic algorithm is called fast approximate subspac e tracking (FAST). The algorithm is derived for the special case in which t he matrix is changed by deleting;the oldest column, shifting the remaining columns to the left, and adding a new column on the right. A second algorit hm (FAST2) is specified by modifying FAST to trade reduced accuracy for hig her speed. The speed and accuracy are compared with the PL algorithm, the P AST and PASTd algorithms, and the FST algorithm, An extension to multicolum n updates for the FAST algorithm is also discussed.