Jacobi method to a system with a tolerance - iteration

Question

Evening all, I have had a similar issue previously with this type of code however I have not been able to figure this one out. I am trying to run my Jacobi code with an initial approximation of the 0 vector, and with tolerance Matrix norm (X^n - x^(n-1)) < 1e^-2
restart;
jacobi:=proc(A::Matrix,b::Vector,x0::Vector,m::integer)
local n,i,j,S,x::Vector,x1::Vector;
x1:=Vector(x0); x := Vector(m);
ee:= LinearAlgebra[VectorNorm](x-x1);
for n from 1 to 50 while ee < 1e-2 do
for i from 1 to m do
S:=0.0;
for j from 1 to m do
if j<>i then S:=S+A[i,j]*x1[j]; end if;
end do;
x[i]:=(-S+b[i])/A[i,i];
end do;
for j from 1 to m do
x1[j]:=x[j];
end do;
print(n,x);
end do;
return x
end proc;
A:=Matrix([[12.4,0.3,-2.2,0.2,3.6],[1.2,7.1,-1.7,-1.6,0.9],[1.3,3.1,10.8,2.2,0.7],[-1.4,0.8,1.1,-7.7,-1.8],[2.8,6.4,0.0,-1.2,-16.6]]);
b:=Vector([-3.5,19.58,-24.56,8.16,-9.28]);
x0:=Vector([0,0,0,0,0]);
jacobi(A,b,x0,5);
#Error, (in jacobi) Vector index out of range
Error, (in LinearAlgebra:-Norm) expects its 1st argument, A, to be of type {Matrix, Vector}, but received x-x1

Answer 1

I found a solution!
restart;
jacobi:=proc(A::Matrix,b::Vector,x0::Vector,m::integer,N::integer,tol::float)
local n,i,j,S,ee,x::Vector,x1::Vector;
x1:=Vector(x0); x := Vector(m); n:=1;
do
for i from 1 to m do
S:=0.0;
for j from 1 to i-1 do
S:=S+A[i,j]*x1[j]
end do;
for j from i+1 to m do
S:=S+A[i,j]*x1[j]
end do;
x[i]:=(-S+b[i])/A[i,i];
end do;
ee:= LinearAlgebra[VectorNorm](x-x1);
if(ee<tol) then
printf("The solution after %d iterations is:",n);
print(x);
break;
end if;
for j from 1 to m do
x1[j]:=x[j];
end do;
n:=n+1;
if (n>N) then error("No convergence after",N,"iterations") end if;
end do;
return x;
end proc;
jacobi := proc(A::Matrix, b::Vector, x0::Vector, m::integer,
N::integer, tol::float)
...
end;
A:=Matrix([[12.4,0.3,-2.2,0.2,3.6],[1.2,7.1,-1.7,-1.6,0.9],[1.3,3.1,10.8,2.2,0.7],[-1.4,0.8,1.1,-7.7,-1.8],[2.8,6.4,0.0,-1.2,-16.6]]);
b:=Vector([-3.5,19.58,-24.56,8.16,-9.28]);
x0:=Vector([0,0,0,0,0]);
jacobi(A,b,x0,5,100,0.01);
The solution after 8 iterations is: