MaplePrimes - answers and comments on Question, Condition of Jacobi Iteration

sum -> add

Joe Riel — Tue, 13 Dec 2011 08:57:23 Z

Change ?sum to ?add and remove the forward-quotes from A. The sum procedure is intended for indefinite summation. You can also delete the two statements, i::nonnegint; and j::nonnegint. They have no effect on the operation. For this procedure to work, the LinearAlgebra package must have been "withed". A better design is to add the statement

uses LinearAlgebra;

at the start of the body of the procedure. See ?uses. Actually, since you use but one procedure from the LinearAlgebra package, it is easy enough to call ColumnDimension with LinearAlgebra:-ColumnDimension. An alternative is to use the new command, ?upperbound. Do

dimA := upperbound(A,2);

diagonally dominant

Pseudomodo — Tue, 13 Dec 2011 10:14:26 Z

The test should occur within the loop, because you have test every row. The procedure can return as soon as it determines failure of the test for any particular row.

JacobiCondition:= proc(A)
     local MC, i, j, DimA;
     DimA:=LinearAlgebra:-ColumnDimension(A);
     for i from 1 to DimA do:
        if add(abs(A[i,j]),j=1..DimA) >= 2*abs(A[i,i]) then
           print("It's Not OK");
           return NULL;
        end if;
     end do;
     print("It's OK");
     return NULL;
end proc:

You should consider applying evalf around the references A[i,i] and A[i,j], so that it can work for Matrices with entries like sqrt(2).

I got it. Thanks so much for helping me.

Tiamosg — Tue, 13 Dec 2011 12:11:54 Z

I got it. Thanks so much for helping me.