Interval algorithm for absolute value equations

DOI10.2478/s11533-011-0067-2zbMath1236.65047OpenAlexW2084109373MaRDI QIDQ657417

Yongkun Deng, Aixiang Wang, Hai-Jun Wang

Publication date: 16 January 2012

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s11533-011-0067-2

zbMATH Keywords

linear complementarity problemerror estimationinterval iterationgeneralized Newton methodabsolute value equation\(\varepsilon\)-inflation

Mathematics Subject Classification ID

Interval and finite arithmetic (65G30) Linear equations (linear algebraic aspects) (15A06)

Related Items (9)

Modified bas iteration method for absolute value equation ⋮ A modified fixed point iteration method for solving the system of absolute value equations ⋮ Inexact Newton-type method for solving large-scale absolute value equation \(Ax-|x|=b\). ⋮ Picard splitting method and Picard CG method for solving the absolute value equation ⋮ A modified multivariate spectral gradient algorithm for solving absolute value equations ⋮ Weaker convergent results of the generalized Newton method for the generalized absolute value equations ⋮ Bounds for the solutions of absolute value equations ⋮ Levenberg-Marquardt method for solving systems of absolute value equations ⋮ A quadratically convergent descent method for the absolute value equation \(Ax + B |x| = b\)

Uses Software

• INTLAB

Cites Work

• A globally and quadratically convergent method for absolute value equations
• Smoothing functions and smoothing Newton method for complementarity and variational inequality problems
• On unique solvability of the absolute value equation
• Systems of linear interval equations
• Absolute value equations
• Absolute value programming
• A residual existence theorem for linear equations
• A generalized Newton method for absolute value equations
• Knapsack feasibility as an absolute value equation solvable by successive linear programming
• Global and finite convergence of a generalized Newton method for absolute value equations
• On the solution of interval linear systems
• Interval analysis: Theory and applications
• Epsilon-inflation in verification algorithms
• Verified solution of large systems and global optimization problems
• On equivalent reformulations for absolute value equations
• A Test for Existence of Solutions to Nonlinear Systems
• Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities
• A theorem of the alternatives for the equationAx+B|x| =b
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