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

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RAHUL KUMAR
RAHUL KUMAR 2019-8-6
编辑： KALYAN ACHARJYA 2019-8-6
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

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KALYAN ACHARJYA
KALYAN ACHARJYA 2019-8-6
编辑：KALYAN ACHARJYA 2019-8-6
>> 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.

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