An extension of the Cayley transform method for a parameterized generalized inverse eigenvalue problem Article Swipe

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Zeynab Dalvand , Masoud Hajarian , José E. Román ·

YOU? · · 2020 · Open Access · · DOI: https://doi.org/10.1002/nla.2327

Summary Since recent studies have shown that the Cayley transform method can be an effective iterative method for solving the inverse eigenvalue problem, in this work, we consider using an extension of it for solving a type of parameterized generalized inverse eigenvalue problem and prove its locally quadratic convergence. This type of inverse eigenvalue problem, which includes multiplicative and additive inverse eigenvalue problems, appears in many applications. Also, we consider the case where the given eigenvalues are multiple. In this case, we describe a modified problem that is not overdetermined and discuss the extension of the Cayley transform method for this modified problem. Finally, to demonstrate the effectiveness of these algorithms, we present some numerical examples to show that the proposed methods are practical and efficient.

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Mathematics Eigenvalues and eigenvectors Parameterized complexity Inverse iteration Inverse Divide-and-conquer eigenvalue algorithm Cayley transform Overdetermined system Extension (predicate logic) Eigendecomposition of a matrix Convergence (economics) Applied mathematics Rayleigh quotient iteration Iterative method Mathematical optimization Algorithm Discrete mathematics Power iteration Computer science Graph Line graph Physics Economic growth Programming language Economics Voltage graph Geometry Quantum mechanics

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Type: article
Language: en
Landing Page: https://doi.org/10.1002/nla.2327
PDF: https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.2327
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Cited By: 6
References: 37
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DOI: https://doi.org/10.1002/nla.2327

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Title: An extension of the Cayley transform method for a parameterized generalized inverse eigenvalue problem

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Language: en

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Publication year: 2020

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Authors: Zeynab Dalvand, Masoud Hajarian, José E. Román

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Landing page: https://doi.org/10.1002/nla.2327

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Concepts: Mathematics, Eigenvalues and eigenvectors, Parameterized complexity, Inverse iteration, Inverse, Divide-and-conquer eigenvalue algorithm, Cayley transform, Overdetermined system, Extension (predicate logic), Eigendecomposition of a matrix, Convergence (economics), Applied mathematics, Rayleigh quotient iteration, Iterative method, Mathematical optimization, Algorithm, Discrete mathematics, Power iteration, Computer science, Graph, Line graph, Physics, Economic growth, Programming language, Economics, Voltage graph, Geometry, Quantum mechanics

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Cited by: 6

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Citations by year (recent): 2025: 2, 2024: 2, 2021: 2

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primary_location.raw_source_name	Numerical Linear Algebra with Applications
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publication_year	2020
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