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math.NA2024
A subspace method for large-scale trace ratio problems
G. Ferrandi, M. E. Hochstenbach, M. R. Oliveira
A subspace method is introduced to solve large-scale trace ratio problems. This approach is matrix-free, requiring only the action of the two matrices involved in the trace ratio.…
math.NA2022
A homogeneous Rayleigh quotient with applications in gradient methods
Giulia Ferrandi, Michiel E. Hochstenbach
Given an approximate eigenvector, its (standard) Rayleigh quotient and harmonic Rayleigh quotient are two well-known approximations of the corresponding eigenvalue. We propose a ne…
math.NA2022
A harmonic framework for stepsize selection in gradient methods
Giulia Ferrandi, Michiel E. Hochstenbach, Natasa Krejic
We study the use of inverse harmonic Rayleigh quotients with target for the stepsize selection in gradient methods for nonlinear unconstrained optimization problems. This provides…