A homogeneous Rayleigh quotient with applications in gradient methods

Giulia Ferrandi; Michiel E. Hochstenbach

doi:10.1016/j.cam.2023.115440

A homogeneous Rayleigh quotient with applications in gradient methods

Giulia Ferrandi (Corresponding author), Michiel E. Hochstenbach

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

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Given an approximate eigenvector, its (standard) Rayleigh quotient and harmonic Rayleigh quotient are two well-known approximations of the corresponding eigenvalue. We propose a new type of Rayleigh quotient, the homogeneous Rayleigh quotient, and analyze its sensitivity with respect to perturbations in the eigenvector. Furthermore, we study the inverse of this homogeneous Rayleigh quotient as stepsize for the gradient method for unconstrained optimization.
The notion and basic properties are also extended to the generalized eigenvalue problem.

Originele taal-2	Engels
Artikelnummer	115440
Aantal pagina's	15
Tijdschrift	Journal of Computational and Applied Mathematics
Volume	437
DOI's	https://doi.org/10.1016/j.cam.2023.115440
Status	Gepubliceerd - feb. 2024

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We are grateful to the referees for their very useful suggestions which considerably improved the quality of the paper. This work has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 812912. We are grateful to the referees for their very useful suggestions which considerably improved the quality of the paper. This work has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 812912 .

Financiers	Financiernummer
European Union’s Horizon Europe research and innovation programme
H2020 Marie Skłodowska-Curie Actions	812912
European Union’s Horizon Europe research and innovation programme

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abstract = "Given an approximate eigenvector, its (standard) Rayleigh quotient and harmonic Rayleigh quotient are two well-known approximations of the corresponding eigenvalue. We propose a new type of Rayleigh quotient, the homogeneous Rayleigh quotient, and analyze its sensitivity with respect to perturbations in the eigenvector. Furthermore, we study the inverse of this homogeneous Rayleigh quotient as stepsize for the gradient method for unconstrained optimization.The notion and basic properties are also extended to the generalized eigenvalue problem.",

keywords = "Eigenvalue problem, Generalized eigenvalue problem, Homogeneous Rayleigh quotient, Projective coordinates, Secant condition, Unconstrained optimization",

author = "Giulia Ferrandi and Hochstenbach, {Michiel E.}",

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AU - Hochstenbach, Michiel E.

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KW - Generalized eigenvalue problem

KW - Homogeneous Rayleigh quotient

KW - Projective coordinates

KW - Secant condition

KW - Unconstrained optimization

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A homogeneous Rayleigh quotient with applications in gradient methods

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