Stable Computation of Generalized Matrix Functions via Polynomial Interpolation∗
نویسنده
چکیده
Generalized matrix functions (GMFs) extend the concept of a matrix function to rectangular matrices via the singular value decomposition. Several applications involving directed graphs, Hamiltonian dynamical systems, and optimization problems with low-rank constraints require the action of a GMF of a large, sparse matrix on a vector. We present a new method for applying GMFs to vectors based on Chebyshev interpolation. The method is matrix-free and requires no orthogonalization. We prove that our method is backward stable and show that it is competitive with existing approaches based on Lanczos bidiagonalization.
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