What is Jacobi method

How Can i write a program for Jacobi method un MATLAB

[Walter Roberson]

https://www.mathworks.com/matlabcentral/fileexchange/63167-gauss-seidel-method-jacobi-method

https://www.mathworks.com/matlabcentral/fileexchange/71043-jacobi-method-solution-of-matrix-equation

Answer 1

[Radu Trimbitas]

See the following source:

function [x,ni]=Jacobi(A,b,x0,err,nitmax)

%JACOBI Jacobi method

%call [x,ni]=Jacobi(A,b,x0,err,nitmax)

%parameters

%A - system matrix

%b - right hand side vector

%x0 - starting vector

%err - tolerance (default 1e-3)

%nitmax - maximum number of iterations (default 50)

%x - solution

%ni -number of actual iterations

%parameter check

if nargin < 5, nitmax=50; end

if nargin < 4, err=1e-3; end

if nargin <3, x0=zeros(size(b)); end

[m,n]=size(A);

if (m~=n) | (n~=length(b))

error('ilegal size')

end

%compute T and c (prepare iterations)

M=diag(diag(A));

N=M-A;

x=x0(:);

for i=1:nitmax

x0=x;

x=M\(N*x0+b); %x=T*x0+c;

if norm(x-x0,inf)<err*norm(x,inf)

ni=i;

return

end

end

error('iteration number exceeded')