A bibliography of the ABS methods

DOI10.1080/10556789708805674zbMath0894.90136OpenAlexW2102980337MaRDI QIDQ4380566

Silvia Nicolai, Emilio Spedicato

Publication date: 17 March 1998

Published in: Optimization Methods and Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10556789708805674

zbMATH Keywords

ABS methodscomplete bibliography

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Numerical computation of solutions to systems of equations (65H10) Linear programming (90C05) Iterative numerical methods for linear systems (65F10) General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to operations research and mathematical programming (90-00)

Related Items

New solutions of LR fuzzy linear systems using ranking functions and ABS algorithms, ABS algorithms for linear equations and optimization

Uses Software

• ESSL

Cites Work

• Restart row update ABS methods for solving systems of nonlinear equations
• Ten years of ABS methods: A review of theoretical results and computational achievements
• A class of scaled direct methods for linear systems
• Truncated nonlinear ABS algorithm and its convergence property
• On the numerical stability of Huang's and related methods
• A class of direct methods for linear systems
• Multi-step nonlinear ABS methods and their efficiency analysis
• Superlinear convergence theorem in the ABSg class of algorithms for nonlinear algebraic equations
• Numerical experiments with ABS algorithms for linear systems on a parallel machine
• Variationally derived algorithms in the ABS class for linear systems
• Solving sparse linear systems by an ABS-method that corresponds to LU- decomposition
• A note on the condition for convergence of nonlinear ABS method
• Analysis of error propagation in the ABS class for linear systems
• A direct method for the general solution of a system of linear equations
• Optimally conditioned scaled ABS algorithms for linear systems
• Convergence analysis of the nonlinear block scaled ABS methods
• A local convergence theorem for nonlinear ABS algorithms
• Solution of linear least squares via the ABS algorithm
• Solving linear least squares by orthogonal factorization and pseudoinverse computation via the modified Huang algorithm in the ABS class
• Quasi-Newton ABS methods for solving nonlinear algebraic systems of equations
• An algorithm for solving determined or undetermined, pull or deficient rank linear systems based upon the optimally conditioned ABS algorithm
• ABS algorithms from Luoyang to beijing
• Numerical experiments with the symmetric algorithm in the ABS class for linear systems
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