Hybrid manipulations for the solution of systems of nonlinear algebraic equations

DOI10.2977/prims/1195182438zbMath0543.65026OpenAlexW2025751258MaRDI QIDQ796256

Satoshi Watanabe

Publication date: 1983

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195182438

zbMATH Keywords

quadratic convergencesecant methodmultiple rootssymbolic manipulationsFORTRANdeflation algorithmhybrid manipulationNewton- Raphson methodNonlinear Algebraic Equation's SolverREDUCE 2singular Jacobian matrices

Mathematics Subject Classification ID

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

Related Items (3)

Modified deflation algorithm for the solution of singular problems. I. A system of nonlinear algebraic equations ⋮ Modified deflation algorithm for the solution of singular problems. II: Nonlinear multipoint boundary value problems ⋮ On the quadratic convergence properties of the epsilon-secant method for the solution of a system of nonlinear equations and its application to a chemical reaction problem

Uses Software

• REDUCE

Cites Work

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• Deflation algorithm for the multiple roots of a system of nonlinear equations
• On the quadratic convergence properties of the epsilon-secant method for the solution of a system of nonlinear equations and its application to a chemical reaction problem
• Structure analyses for large scale nonlinear multipoint boundary value problems
• Starlike domains of convergence for Newton's method at singularities
• Multipoint boundary value problems with discontinuities. II. Convergence of the initial value adjusting method
• On quadratic convergence of the initial value adjusting method for nonlinear multipoint boundary value problems
• On the convergence of the initial-value adjusting method for nonlinear boundary value problems
• The initial-value adjusting method for problems of the least squares type of ordinary differential equations
• Initial-value adjusting method for the solution of nonlinear multipoint boundary-value problems
• Convergence of the Newton process to multiple solutions
• Widely Convergent Method for Finding Multiple Solutions of Simultaneous Nonlinear Equations
• Newton’s Method at Singular Points. I
• Newton’s Method for Singular Problems when the Dimension of the Null Space is $>1$
• On Newton’s Method for Singular Problems
• On the application of Newton's method in a singular case

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