A numerical method for branch points of a system of nonlinear algebraic equations

DOI10.1016/0168-9274(88)90018-9zbMath0646.65045OpenAlexW1968704649MaRDI QIDQ1104048

Takeo Ojika

Publication date: 1988

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(88)90018-9

zbMATH Keywords

numerical exampleNewton's methodGaussian eliminationbranch pointssystem of nonlinear algebraic equations

Mathematics Subject Classification ID

Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

Related Items (8)

A heuristic method for certifying isolated zeros of polynomial systems ⋮ Improved two-step Newton's method for computing simple multiple zeros of polynomial systems ⋮ Newton-Anderson at Singular Points ⋮ A new deflation method for verifying the isolated singular zeros of polynomial systems ⋮ Modified deflation algorithm for the solution of singular problems. I. A system of nonlinear algebraic equations ⋮ Newton's method with deflation for isolated singularities of polynomial systems ⋮ On isolation of simple multiple zeros and clusters of zeros of polynomial systems ⋮ Verified error bounds for singular solutions of nonlinear systems

Uses Software

• REDUCE
• MACSYMA

Cites Work

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• 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
• Deflation algorithm for the multiple roots of a system of nonlinear equations
• Direction of branches bifurcating at a bifurcation point. Determination of starting points for a continuation algorithm
• Structure analyses for large scale nonlinear multipoint boundary value problems
• A comparison of methods for determining turning points of nonlinear equations
• Numerical computation of periodic orbits that bifurcate from stationary solutions of ordinary differential equations
• Evaluation of branching points for nonlinear boundary-value problems based on the GPM technique
• An efficient algorithm for the determination of certain bifurcation points
• Numerical computational of branch points in nonlinear equations
• Evaluation of limit and bifurcation points for algebraic equations and nonlinear boundary-value problems
• Bifurcation from simple eigenvalues
• The Computation of Symmetry-Breaking Bifurcation Points
• A Method for the Numerical Determination of Bifurcation States of Nonlinear Systems of Equations
• Numerical Methods for a Class of Finite Dimensional Bifurcation Problems
• Numerical computation of branch points in ordinary differential equations

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