Numerical linear algebra | Relaxation (iterative methods)

Jacobi method

In numerical linear algebra, the Jacobi method is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi. (Wikipedia).

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Newton's Method for Systems of Nonlinear Equations

Generalized Newton's method for systems of nonlinear equations. Lesson goes over numerically solving multivariable nonlinear equations step-by-step with visual examples and explanation of the Jacobian, the backslash operator, and the inverse Jacobian. Example code in MATLAB / GNU Octave on

From playlist Newton's Method

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Approximating the Jacobian: Finite Difference Method for Systems of Nonlinear Equations

Generalized Finite Difference Method for Simultaneous Nonlinear Systems by approximating the Jacobian using the limit of partial derivatives with the forward finite difference. Example code on GitHub https://www.github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:13 Prerequisites 0:3

From playlist Solving Systems of Nonlinear Equations

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Mod-01 Lec-28 Jacobi Method

Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics

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MATLAB Solves the Laplace Equation (Iterative Method) | Lecture 68 | Numerical Methods for Engineers

How to solve the Laplace equation using the Jacobi method. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?su

From playlist Numerical Methods for Engineers

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Marianne Akian: "Probabilistic max-plus schemes for solving Hamilton-Jacobi-Bellman equations"

High Dimensional Hamilton-Jacobi PDEs 2020 Workshop I: High Dimensional Hamilton-Jacobi Methods in Control and Differential Games "Probabilistic max-plus schemes for solving Hamilton-Jacobi-Bellman equations" Marianne Akian - Institut National de Recherche en Informatique et Automatique (

From playlist High Dimensional Hamilton-Jacobi PDEs 2020

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Theory of numbers: Jacobi symbol

This lecture is part of an online undergraduate course on the theory of numbers. We define the Jacobi symbol as an extension of the Legendre symbol, and show how to use it to calculate the Legendre symbol fast. We also briefly mention the Kronecker symbol. For the other lectures in t

From playlist Theory of numbers

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Intro to the Jacobian

Gentle example explaining how to compute the Jacobian. Free ebook http://tinyurl.com/EngMathYT

From playlist Several Variable Calculus / Vector Calculus

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Yat Tin Chow: "A numerical method of solving high dimensional Hamilton-Jacobi equations with gen..."

High Dimensional Hamilton-Jacobi PDEs 2020 Workshop I: High Dimensional Hamilton-Jacobi Methods in Control and Differential Games "A numerical method of solving high dimensional Hamilton-Jacobi equations with generalized Hopf-Lax formula" Yat Tin Chow - University of California, Riverside

From playlist High Dimensional Hamilton-Jacobi PDEs 2020

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Jacobian matrix example

Gentle example showing how to compute the Jacobian. Free ebook http://tinyurl.com/EngMathYT

From playlist Several Variable Calculus / Vector Calculus

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Lecture: Eigen-decompositions and Iterations

We develop a theoretical approach to understanding how eigen-decompositions of matrices can be used in iterative schemes for Ax=b.

From playlist Beginning Scientific Computing

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Jacobi, Gauss-Seidel and SOR Methods | Lecture 66 | Numerical Methods for Engineers

Iterative methods for solving the discrete Laplace equation. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?

From playlist Numerical Methods for Engineers

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CMPSC/Math 451. March 20, 2015. Gauss-Seidel, SOR. Wen Shen

Wen Shen, Penn State University Lectures are based on my book: "An Introduction to Numerical Computation", published by World Scientific, 2016. See promo video: https://youtu.be/MgS33HcgA_I

From playlist Numerical Computation spring 2015. Wen Shen. Penn State University.

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Lec 15 | MIT 18.086 Mathematical Methods for Engineers II

Iterative Methods and Preconditioners View the complete course at: http://ocw.mit.edu/18-086S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.086 Mathematical Methods for Engineers II, Spring '06

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Wheatstone Bridge: A (Not So) Honorable History

Charles Wheatstone introduced "his" bridge in 1843 but it was first invented in 1833 by Samuel Christie. This is the story of *why* these men invented this device and the convoluted tale of how it got its name. Links: My mailing list: https://kathylovesphysics.ck.page/welcome My Patreo

From playlist "The Lightning Tamers": A History of Electricity

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Mod-01 Lec-29 Gauss-Seidel Method

Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics

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Lecture: Iteration Methods for Ax-b

This details how to apply a simple iteration procedure for solving Ax=b, including Jacobi iterations and Gauss-Siedel modifications.

From playlist Beginning Scientific Computing

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Victorita Dolean: An introduction to domain decomposition methods - lecture1

HYBRID EVENT Recorded during the meeting "Domain Decomposition for Optimal Control Problems" the September 05, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematici

From playlist Jean-Morlet Chair - Gander/Hubert

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The Jacobian matrix

An introduction to how the jacobian matrix represents what a multivariable function looks like locally, as a linear transformation.

From playlist Multivariable calculus

Related pages

Diagonally dominant matrix | Spectral radius | Successive over-relaxation | Iterative method | System of linear equations | Jacobi eigenvalue algorithm | Carl Gustav Jacob Jacobi | Diagonal matrix | Belief propagation | Condition number | Matrix splitting | Gauss–Seidel method | Numerical linear algebra