The local convergence of ABS methods for nonlinear algebraic equations

DOI10.1007/BF01397545zbMath0609.65038OpenAlexW2074033977MaRDI QIDQ1086988

Aurel Galantai, Emilio Spedicato, Jozsef Abaffy

Publication date: 1987

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133204

zbMATH Keywords

local convergenceiterative processesnonlinear algebraic systemsABS classsuperlinear Q-rate of convergence

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10)

Related Items (20)

Quasi-Newton ABS methods for solving nonlinear algebraic systems of equations ⋮ On systolic general system solution for optimal artificial neural network training ⋮ Reconstructing a matrix from a partial sampling of Pareto eigenvalues ⋮ An ABS algorithm for solving singular nonlinear systems with rank defects. ⋮ Parallel ABS projection methods for linear and nonlinear systems with block arrowhead structure ⋮ Modification of trigonometric collocation method for impulsive periodic BVP ⋮ Restart row update ABS methods for solving systems of nonlinear equations ⋮ Variations on the Gram--Schmidt and the Huang algorithms for linear systems: A numerical study ⋮ A note on the condition for convergence of nonlinear ABS method ⋮ An adaptive learning rate backpropagation‐type neural network for solving n × n systems on nonlinear algebraic equations ⋮ Solution of linear least squares via the ABS algorithm ⋮ A class of scaled direct methods for linear systems ⋮ Truncated nonlinear ABS algorithm and its convergence property ⋮ A FAST conic method for function minimization ⋮ A ABS algorithm for solving singular nonlinear system with space transformation ⋮ A new nonlinear ABS-type algorithm and its efficiency analysis^∗ ⋮ ABS algorithms for linear equations and optimization ⋮ Multi-step nonlinear ABS methods and their efficiency analysis ⋮ Superlinear convergence theorems for Newton-type methods for nonlinear systems of equations ⋮ Convergence analysis of the nonlinear block scaled ABS methods

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