Orthogonal iterations on Structured Pencils

04/22/2021

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by   Roberto Bevilacqua, et al.

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We present a class of fast subspace tracking algorithms based on orthogonal iterations for structured matrices/pencils that can be represented as small rank perturbations of unitary matrices. The algorithms rely upon an updated data sparse factorization – named LFR factorization – using orthogonal Hessenberg matrices. These new subspace trackers reach a complexity of only O(nk^2) operations per time update, where n and k are the size of the matrix and of the small rank perturbation, respectively.