Generalized Perron Roots and Solvability of the Absolute Value Equation

DOI10.1137/22m1517184arXiv1912.08157OpenAlexW2995714732MaRDI QIDQ6066098

Josué Tonelli-Cueto, Manuel Radons

Publication date: 15 November 2023

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.08157

zbMATH Keywords

linear complementarity problemdegree theoryabsolute value equationaligned spectrumgeneralized Perron roots

Mathematics Subject Classification ID

Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Matrix equations and identities (15A24) Numerical methods for mathematical programming, optimization and variational techniques (65K99)

Cites Work

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• Systems of linear interval equations
• Absolute value equations
• Q-matrices and spherical geometry
• \(Q\)-matrix recognition via secondary and universal polytopes
• The P-matrix problem is co-NP-complete
• Theorems of Perron-Frobenius type for matrices without sign restrictions
• On \(P\)-matrices
• Error bounds and a condition number for the absolute value equations
• A Homological Characterization of Q-Matrices
• Condition
• The Linear Complementarity Problem
• Iterative Solution of Piecewise Linear Systems
• Interval Methods for Systems of Equations
• The Perron-Frobenius theorem for homogeneous, monotone functions
• Matrices with eigenvectors in a given subspace

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