Gauss-Seidel Method of Solving Simultaneous Linear Equations: Example: Part 2 of 2

Learn via example how Gauss-Seidel method of solving simultaneous linear equations works.

Category:

Education

Tags:

• Gauss
• Seidel
• Method
• Simultaneous
• Linear
• Equations
• numerical
• methods
• numericalmethodsguy

[rickycax]

hello,very nice work here,thank you.

what if teacher ask question which doesnt have starting values? what should we do then , take for starting value? [0,0,0] ? prof. just gives the system and ask solve this system "using Seidel iteration 3 steps."

[numericalmethodsguy]

@rickycax Unless you know the physics of the problem, an initial guess of [0,0,0] is as good as any.

[arqi25]

x1 − x2 + 3x3 = 4

5x1 + 3x2 + x3 = 0

−x1 + 4x2 − 2x3 = 1

why we cannot use this system using gauss-seidel method and how do we re-arrange it? how would you know when to re-arrange a system, if you please answer these questions I'll be very grateful.

[rickycax]

@rickycax and what if what is teacher gives variables as x,y,z it still works?

[Utkuaksar]

thank you very much. I hadn't understood but I can solve through that video

[mdeenny]

@rizwansahimy lambda is a question for gauss seidel with relaxation, try find topic about that... this video is about the basic of gauss seidel method

[rizwansahimy]

my question have a lambda how to solve that?

[Elite1666]

thank a lot!

[srajan0929]

this is a very long method, you should employ the splitting technique, i.e A = M+N

with M = D + L and N = U, hence:

X(n+1) = -(D+L)^-1 (Uxn) + (D+L)^-1 * b

using the recursion xn+1 = Rxn + b

[Zhazhael]

Nice english!!! XD