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Generalized Davidson and multidirectional-type methods for the generalized singular value decomposition. (arXiv:1705.06120v1 [math.NA])
来源于:arXiv
We propose new iterative methods for computing nontrivial extremal
generalized singular values and vectors. The first method is a generalized
Davidson-type algorithm and the second method employs a multidirectional
subspace expansion technique. Essential to the latter is a fast truncation step
designed to remove a low quality search direction and to ensure moderate growth
of the search space. Both methods rely on thick restarts and may be combined
with two different deflation approaches. We argue that the methods have
monotonic and (asymptotic) linear convergence, derive and discuss locally
optimal expansion vectors, and explain why the fast truncation step ideally
removes search directions orthogonal to the desired generalized singular
vector. Furthermore, we identify the relation between our generalized
Davidson-type algorithm and the Jacobi--Davidson algorithm for the generalized
singular value decomposition. Finally, we generalize several known convergence
results for the Hermitian 查看全文>>