Efficient, Numerically Stabilized Rank-One Eigenstructure Up.dating

Rank-one eigenvalue decomposition (EVD) updating is well suited to the problem of tracking time-varying subspaces. Previ- ously published rank-one EVD updating algorithms suffer from a lin- ear buildup of roundoff error which makes them impractical for large numbers of recursive updates. The main contribution of this paper is the development of a numerical stabilization technique which elimi- nates the error buildup problem in a computationally efficient manner and makes the rank-one EVD update a practical numerical tool for on- line computation. A simplified eigenvalue iteration is also given which reduces the complexity of the algorithm somewhat as well as the com- putation time. Simulations are presented to illustrate numerical per- formance.

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