Concept

Banach fixed-point theorem

Related lectures (29)

Covers the Picard method for solving nonlinear equations using fixed point iteration.

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Explores the numerical analysis of nonlinear equations, focusing on convergence criteria and methods like bisection and fixed-point iteration.

Explores the convergence of fixed point methods and the implications of different convergence rates.

Explores Newton's method for finding roots of nonlinear equations and its interpretation as a second-order method.

Explores the fixed point method for global convergence in solving nonlinear equations.

Covers fixed point methods and the Picard method for solving nonlinear equations iteratively.

Explores applying fixed point methods to solve electrical circuit equations and find diode voltage.

Explores the resolution of ODEs and the Banach fixed-point theorem.

Introduces the fixed point method for solving nonlinear equations by transforming the problem into an equivalent form.

Covers Newton's method for finding zeros of functions through fixed point iteration and discusses convergence properties.

Covers the local inverse theorem, diffeomorphisms, contraction mappings, and the Jacobian determinant.

Explores the Banach Fixed Point Theorem, showing the uniqueness of fixed points in contraction mappings.

Focuses on fixed points in graph theory and their implications in algorithms and analysis.

Explores the Newton method for systems and fixed point iterations, discussing convergence and properties.

Explores nonlinear equations, bisection, fixed-point methods, error control, and graphical interpretations of fixed points.

Covers fixed point methods for finding zeros of non-linear equations.

Explores the global convergence of the fixed point method for nonlinear equations.

Explores fixed point methods for non-linear equations and dynamic models in MATLAB.

Covers the fixed point method for solving nonlinear equations and discusses convergence properties.