here is my full worksheet: > > restart; > with(LinearAlgebra): > A:=LinearAlgebra:-RandomMatrix(6,5); > Transpose(A); > M:=Transpose(A).A; > u[0]:=LinearAlgebra:-RandomVector[column](5); > b:=LinearAlgebra:-RandomVector[column](6); > p:=LinearAlgebra:-RandomVector[column](5); > w:=1.3; > e:=0.2; > u[i+1][k]:=u[i][k]-w*(1/(M[k,k]))*((sum(M[k,j]*u[i][j],j=1..5))+e*b[k]+(sum(A[k,j]*p[j],j=1..5))-(sum(M[k,j]*u[i+1][j],j=1..k-1))+(sum(M[k,j]*u[i][j],j=1..k-1))); basically i am working in low dimensions just to try to get my algorithm working. i planned on stating the algorithm and then introducing a loop, something along the lines of: for k from 1 to 5 do for i from 1 to 10 do u[i+1][k]; end do; end do; again i must state that i am a maple novice (as if you hadn't guessed). i'm not sure if what i had planned is even possible or if i am going about this the right way, so any help would be greatly appreciated. thank you.

here is my full worksheet: > > restart; > with(LinearAlgebra): > A:=LinearAlgebra:-RandomMatrix(6,5); > Transpose(A); > M:=Transpose(A).A; > u[0]:=LinearAlgebra:-RandomVector[column](5); > b:=LinearAlgebra:-RandomVector[column](6); > p:=LinearAlgebra:-RandomVector[column](5); > w:=1.3; > e:=0.2; > u[i+1][k]:=u[i][k]-w*(1/(M[k,k]))*((sum(M[k,j]*u[i][j],j=1..5))+e*b[k]+(sum(A[k,j]*p[j],j=1..5))-(sum(M[k,j]*u[i+1][j],j=1..k-1))+(sum(M[k,j]*u[i][j],j=1..k-1))); basically i am working in low dimensions just to try to get my algorithm working. i planned on stating the algorithm and then introducing a loop, something along the lines of: for k from 1 to 5 do for i from 1 to 10 do u[i+1][k]; end do; end do; again i must state that i am a maple novice (as if you hadn't guessed). i'm not sure if what i had planned is even possible or if i am going about this the right way, so any help would be greatly appreciated. thank you.