Develop your own M-file function for the Gauss- Seidel method without relaxation based on Fig. 12.2, but change the first line so that it returns the approximate error and the number of iterations:

function [x,ea,iter] = ...
Gauss Seidel (A,b,es, maxit)

Test it by duplicating Example 12.1 and then use it to solve Prob. 12.2a.

Example 12.1

Data From Problem 12.2

(a) Use the Gauss-Seidel method to solve the following system until the percent relative error falls below ε_s = 5%:

(b) Repeat (a) but use overrelaxation with λ = 1.2.

Transcribed Image Text:

function x = Gauss Seidel (A, b, es, maxit) & GaussSeidel: Gauss Seidel method $ x = GaussSeidel (A,b): Gauss Seidel without relaxation & input: 음.. A = coefficient matrix 8 bright hand side vector 8 es = stop criterion (default = 0.000018) 8 maxit = max iterations (default = 50) $output: 8 x = solution vector if nargin<2, error ('at least 2 input arguments required'), end if nargin<4|isempty (maxit), maxit=50; end if nargin<3 |isempty (es), es=0.00001; end [m, n] = size (A); if m-=n, error ('Matrix A must be square'); end C = A; for i=1:n C(1,1)= 0; x(i) = 0; end x = x¹; for i=1:n C(i, 1:n) = C(1, 1:n)/A (i, i); end for i = 1:n d(i) = b(i)/A (i, i); end iter = 0; while (1) xold = x; for i x(i)= a(i)-C (i, :) *x; if x(i) = 0 ea (i) = abs((x(i) xold (i))/x(i))* 100; end 1:n end iter iter+1; if max (ea) <=es | iter >= maxit, break, end end