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This subtopic introduces the core ideas in nonlinear equations, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
Roots of polynomial equations. This topic studies numerical methods for nonlinear equations, including root-finding, fixed-point iterations, and convergence analysis.
Used to compute zeros and fixed points in nonlinear models.
Numerical computation of solutions to single equations. This topic studies numerical methods for nonlinear equations, including root-finding, fixed-point iterations, and convergence analysis.
Used to compute zeros and fixed points in nonlinear models.
Numerical computation of solutions to systems of equations. This topic studies numerical methods for nonlinear equations, including root-finding, fixed-point iterations, and convergence analysis.
Used to compute zeros and fixed points in nonlinear models.
Continuation and homotopy methods for computing solutions of nonlinear equations. This topic studies numerical methods for nonlinear equations, including root-finding, fixed-point iterations, and convergence analysis.
Used to compute zeros and fixed points in nonlinear models.
Eigenvalue problems for nonlinear operators. This topic studies numerical methods for nonlinear equations, including root-finding, fixed-point iterations, and convergence analysis.
Used to compute zeros and fixed points in nonlinear models.
Global methods, including homotopy approaches to the numerical solution of nonlinear equations. This topic studies numerical methods for nonlinear equations, including root-finding, fixed-point iterations, and convergence analysis.
Used to compute zeros and fixed points in nonlinear models.