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 introduction to the topic. In the introduction, we shall solve the first 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...
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Негізгі бет 🟢10a - Fixed Point Iteration Method for Multivariable Functions (Jacobi and Gauss-Seidel Method) Ex1
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