Efficient, numerically stabilized rank-one eigenstructure updating (signal processing)

Abstract

Rank-one eigenvalue decomposition (EVD) updating is well suited to the problem of tracking time-varying subspaces. Previously published rank-one EVD updating algorithms suffer from a linear buildup of roundoff error, which makes them impractical for a large number of recursive updates. In the present work, the authors develop a numerical stabilization technique, which eliminates the error buildup problem in a computationally efficient manner and makes the rank-one EVD update a practical numerical tool for online computation. A simplified eigenvalue iteration is also given. It reduces the complexity of the algorithm somewhat as well as the computation time. Simulations are presented to illustrate numerical performance.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>