Error in newton rapshon problem. My error in iteration line (err(i))=abs(Y-Yold)

X=[.0014;.0075;.3];
maxiter=100;
tolX=.000001;
Y=X;
Yold=X;
rho_ss=8000;
rho_cop=8960;
% defined thickness
thick_i=.0004;    
thick_o=.00135;
D_i=X(1);D_o=X(2);L=X(3);
%% function value
fval=(((rho_ss*pi*thick_i*D_i*L)+(rho_cop*pi*thick_o*D_o*L))-.05).^2; % objective function
%% putting jacobian function
J=2*[((rho_ss*pi*D_i*thick_i*L+rho_cop*pi*D_o*thick_o*L)-.05)*(rho_ss*pi*thick_i*L);
     ((rho_ss*pi*D_i*thick_i*L+rho_cop*pi*D_o*thick_o*L)-.05)*(rho_cop*pi*thick_o*L);
     ((rho_ss*pi*D_i*thick_i*L+rho_cop*pi*D_o*thick_o*L)-.05)*(rho_ss*pi*thick_i+rho_cop*pi*thick_o)];
 %% hessian function
H=[(rho_ss^2*pi^2*thick_i^2*L^2) (rho_cop*rho_ss*pi^2*thick_i*thick_o*L^2) ((2*rho_ss^2*pi^2*D_i*thick_i^2*L)+(2*rho_ss*rho_cop*pi^2*thick_i*thick_o*L)-(.05*rho_ss*pi*thick_i));
  (rho_ss*rho_cop*pi.^2*thick_i*thick_o*L.^2) (rho_cop.^2*pi.^2*thick_o.^2*L.^2) ((rho_ss*rho_cop*pi.^2*D_i*thick_i*thick_o*L)+(rho_cop.^2*pi.^2*thick_o.^2*2*L)-(.05*rho_cop*pi*thick_o));
   ((rho_ss.^2*pi.^2*2*D_i*thick_i.^2*L)+(2*(rho_cop*rho_ss*pi.^2*D_o*thick_i*thick_o*L))-(.05*rho_ss*pi*thick_i)) (2*(rho_ss*rho_cop*pi.^2*D_i*thick_i*thick_o*L)+(rho_cop.^2*pi.^2*2*D_o*thick_o.^2*L-.05*rho_cop*pi*thick_o))  ((rho_ss.^2*pi.^2*D_i.^2*thick_i.^2)+(2*(rho_cop*rho_ss*pi.^2*D_i*D_o*thick_i*thick_o))+(rho_cop.^2*pi.^2*D_o.^2*thick_o))];   
%% using optimization in newton rapshon
for i=1:maxiter
    Y=Y - (J./H);                     % newton -rapshon
    Yold=Y;
    err(i)=abs(Y-Yold);              % error  iteration
    if (err(i)<tolX)break;
     end
end

[madhan ravi]

You try to stuff a vector as a scalar.

[Walter Roberson]

Perhaps

err(i) = sum(abs(Y-Yold));

but more common would be

err(i) = sum((Y-Yold).^2);

Answer 1

[KALYAN ACHARJYA]

>> whos Y
  Name      Size            Bytes  Class     Attributes
  Y         3x3                72  double              
>> whos Yold
  Name      Size            Bytes  Class     Attributes
  Yold      3x3                72  double              

When I checked it-

Y =
   -0.0249   -0.0056    0.0004
   -0.0188    0.0005    0.0065
   -2.6337   -0.4761    0.2366

And

Yold =
   -0.0249   -0.0056    0.0004
   -0.0188    0.0005    0.0065
   -2.6337   -0.4761    0.2366

Now find the error(i)

>> abs(Y-Yold)
ans =
     0     0     0
     0     0     0
     0     0     0

In each iteration the error (err) will be same because, you cpoying Y to Yold, abs(Y-Yold) becomes 0

Yold=Y;
err(i)=abs(Y-Yold);  

Now you want to save 3x3 (Y-Yold) zero 2D vector (matrix) in an err array, which is not permissible.

May be (not Sure): As per my observation the err(i) should have numeric value. Please debug the code from back onwards, why the Y return as 3x3.

Hope you get the issue.