WHEN I DO INVERSE OF MY MATRIX IT GIVE VERY LARGE VALUE AND MULTIPLICATION OF (inv(H).*J) GIVE INCORRECT VALUE. can you resolve it

X=[.0014;.0075;.3];
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; % 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))];   

Z=inv(H);
W=(J.*inv(H));

Answer 1

[KSSV]

YOur H is a rank deficeint matrix...check

rank(H)

rank of H is 2. Also check it's determinant is zero. So you have only two independent rows/columns in your matrix....Thus your matrix reduces to a rectangular matrix. Try using pinv.