**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# Newton's Method: Convergence Analysis

Description

This lecture covers the convergence analysis of Newton's method for solving nonlinear equations. It explains the convergence properties, including linear and quadratic convergence, and discusses the conditions for convergence. The lecture also introduces the Picard method and the string method as alternative iterative approaches for finding zeros of functions.

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.

Related concepts (135)

Window manager

A window manager is system software that controls the placement and appearance of windows within a windowing system in a graphical user interface. Most window managers are designed to help provide a desktop environment. They work in conjunction with the underlying graphical system that provides required functionality—support for graphics hardware, pointing devices, and a keyboard—and are often written and created using a widget toolkit. Few window managers are designed with a clear distinction between the windowing system and the window manager.

Window

A window is an opening in a wall, door, roof, or vehicle that allows the exchange of light and may also allow the passage of sound and sometimes air. Modern windows are usually glazed or covered in some other transparent or translucent material, a sash set in a frame in the opening; the sash and frame are also referred to as a window. Many glazed windows may be opened, to allow ventilation, or closed, to exclude inclement weather. Windows may have a latch or similar mechanism to lock the window shut or to hold it open by various amounts.

Fixed-point iteration

In numerical analysis, fixed-point iteration is a method of computing fixed points of a function. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of , i.e., More generally, the function can be defined on any metric space with values in that same space.

Window function

In signal processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval, normally symmetric around the middle of the interval, usually approaching a maximum in the middle, and usually tapering away from the middle. Mathematically, when another function or waveform/data-sequence is "multiplied" by a window function, the product is also zero-valued outside the interval: all that is left is the part where they overlap, the "view through the window".

Window (computing)

In computing, a window is a graphical control element. It consists of a visual area containing some of the graphical user interface of the program it belongs to and is framed by a window decoration. It usually has a rectangular shape that can overlap with the area of other windows. It displays the output of and may allow input to one or more processes. Windows are primarily associated with graphical displays, where they can be manipulated with a pointer by employing some kind of pointing device.

Related lectures (347)

Iterative Methods for Nonlinear Equations

Explores iterative methods for solving nonlinear equations, discussing convergence properties and implementation details.

Newton's Method: Fixed Point Iterative Approach

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

Picard Method: Fixed Point Iterative Technique

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

Introduction to LabVIEWME-213: Programmation pour ingénieur

Covers the basics of LabVIEW, including its importance, history, functions, and tools available.

Numerical Analysis: Nonlinear EquationsMATH-251(c): Numerical analysis

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