**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Nonlinear Equations: Fixed Point Method

Description

This lecture covers the topic of nonlinear equations and the fixed point method. It discusses the convergence criteria, behavior of sequences, and stopping criteria for the fixed point method. The instructor explains the process of finding fixed points and the conditions for convergence.

Login to watch the video

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

In course

Instructors (2)

Related concepts (76)

MATH-250: Numerical analysis

Construction and analysis of numerical methods for the solution of problems from linear algebra, integration, approximation, and differentiation.

Related lectures (257)

Partial differential equation

In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

Integral equation

In mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: where is an integral operator acting on u. Hence, integral equations may be viewed as the analog to differential equations where instead of the equation involving derivatives, the equation contains integrals.

Equation

In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of determining which values of the variables make the equality true.

Nonlinear system

In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems.

Nonlinear Equations: Convergence and Taylor Polynomials

Explores nonlinear equations, emphasizing convergence and Taylor polynomials for function approximation.

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.

Newton's Method: Convergence and Criteria

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

Implicit Methods: Retrograde Euler

Covers the retrograde Euler method, an implicit numerical scheme used to solve equations and the concept of convergence order.