Lectures related to Fixed-point iteration

Numerical Analysis: Nonlinear Equations

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

Higher Order Methods: Iterative Techniques

Covers higher order methods for solving equations iteratively, including fixed point methods and Newton's method.

Nonlinear Equations: Fixed Point Method Convergence

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

Picard Method: Fixed Point Iterative Technique

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

Newton's Method: Convergence and Criteria

Explores the Newton method for non-linear equations, discussing convergence criteria and stopping conditions.

Discrete Time Solution: Stability Properties and Fixed Points

Explores stability properties and fixed points in discrete time solutions.

Numerical Methods: Fixed Point and Picard Method

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

Convergence of Fixed Point Methods

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

Scaling & Renormalization in Statistical Mechanics

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

Electrical Circuit: Fixed Point Methods

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

Numerical Analysis: Newton's Method

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

Information Theory: Basics

Covers the basics of information theory, entropy, and fixed points in graph colorings and the Ising model.

Vectorization in Python: Efficient Computation with Numpy

Covers vectorization in Python using Numpy for efficient scientific computing, emphasizing the benefits of avoiding for loops and demonstrating practical applications.

The Banach Fixed Point Theorem

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

Convergence Analysis: Iterative Methods

Covers the convergence analysis of iterative methods and the conditions for convergence.

Stopping Criteria for Fixed Point Iteration

Discusses stopping criteria for fixed point iteration in nonlinear equations and how to manage errors.

Newton's Method: Fixed Point Iterative Approach

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

Stability of Discrete Time Periodic Solutions

Covers the stability of discrete time periodic solutions and their properties.

Nonlinear Equations: Fixed Point Method

Covers the topic of nonlinear equations and the fixed point method.

Nonlinear Equations: Bisection and Fixed-Point Methods

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