🟢10a - Fixed Point Iteration Method for Multivariable Functions (Jacobi and Gauss-Seidel Method) Ex1

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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 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
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Make sure to watch till the end.
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Пікірлер: 6

@risingstars_el 3 ай бұрын

Always on point

@SkanCityAcademy_SirJohn 3 ай бұрын

Thanks so much

@assaineindustries 3 ай бұрын

Master, thanks for the video. I have been using a book that tabulated the iteration values and there's a column of values labelled ||x^k - x^k+1||, can you help me understand how they get values for this column. Many thanks.

@SkanCityAcademy_SirJohn 3 ай бұрын

It's basically called the stopping criteria, one is expected to use the stopping criteria to stop at a number of say n iterations if the number of iterations are not given. So as you realized you have negligible difference ie close to 0 between the next iteration values and the previous iteration values, you can stop there. x^k+1 means next value x^k means previous value