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 functionH=[(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; endend
MATLAB: Error in newton rapshon problem. My error in iteration line (err(i))=abs(Y-Yold)
error in iteration
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