🟢10b - Fixed Point Iteration Method for Multivariable Functions (Jacobi and Gauss-Seidel Method) Ex2

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In this lesson, we shall consider the problem of finding the roots or solutions to fixed-point iteration systems considering systems of nonlinear equations or functions of several variables.
This video covers the second example.
Given a system of nonlinear equations in the form
f1(x1 +x2 +.....xn) = 0
f2(x1 +x2 +.....xn) = 0
.
.
fn(x1 +x2 +.....xn) = 0
we transform each of the root finding problems to fixed-point problems of the form;
x1 = f1(x1 +x2 +.....xn) = 0
x2 = f2(x1 +x2 +.....xn) = 0
.
.
xn = fn(x1 +x2 +.....xn) = 0
00:00 - Introduction
03:00 - Example 1 (Jacobi)
14:09 - Example 1 (Gauss-Seidel)
23:53 - Conclusion
Playlists on various Course
1. Applied Electricity
• APPLIED ELECTRICITY
2. Linear Algebra / Math 151
• LINEAR ALGEBRA
3. Basic Mechanics
• BASIC MECHANICS / STATICS
4. Calculus with Analysis / Calculus 1 / Math 152
• CALCULUS WITH ANALYSIS...
5. Differential Equations / Math 251
• DIFFERENTIAL EQUATIONS
6. Electric Circuit Theory / Circuit Design
• ELECTRIC CIRCUIT THEOR...
7. Calculus with Several Variables
• CALCULUS WITH SEVERAL ...
8. Numerical Analysis
• MATH 351 / NUMERICAL A...
Make sure to watch till the end.
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Пікірлер: 5

@thepassionachievers 6 ай бұрын

Sir John...You do all

@SkanCityAcademy_SirJohn 6 ай бұрын

Thanks so much bro

@hameero7445 3 ай бұрын

One question, please I want to understand why you didn't check if the |derivative g(x,y)|< 1 at x• and y•

@SkanCityAcademy_SirJohn 3 ай бұрын

Usually, trying to prove the convergence from that approach is kind of difficult when solving for several variables unlike single variables, so we assume that it convergence and start to solve

@hameero7445 3 ай бұрын

I get it, Thank you very much @@SkanCityAcademy_SirJohn