Newtons Method but error message “Singular Matrix”
When I tried to solve theta and V with Newton for systems I got this error message
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.765187e-24.
Previously I had no problems just solving theta with Newtons for systems, but adding V got me an ill conditioned matrix. We tried different initial values to see if they were triggering, but all of them lead to the same error message. We would be very grateful for any help we could get!
function [theta,V]= newtonfsys1(theta1,V1)
t=1; it=0; maxit=100;theta0=0;V0=200/3.6;
while norm(t)>1e-9 & it<maxit
%Creates a list of x and y values
[v1,v2,v3,v4,v5]=varden(theta0,V0);
[x0,y0]=rungekutta(v1,v2,v3,v4,v5);
[v1,v2,v3,v4,v5]=varden(theta1,V1);
[x1,y1]=rungekutta(v1,v2,v3,v4,v5);
%checking if condition is being met
for i=1:length(x1)
if (abs(11.8872-x1(i))<0.01) && (abs(18.288-x1(end))<0.01)
break
end
end
for p=1:length(x0)
if (abs(11.8872-x0(p))<0.01) && (abs(18.288-x0(end))<0.01)
break
end
end
% takes the "i" & "p" from the condition and picks a good(hopefully constant for x and y
y1=y1(i)-1.001; y0=y0(p)-1.001; x1=x1(i)-11.8872; x0=x0(p)-11.8872;
%approximate derivative
dxdtheta= (x1-x0)/(theta1-theta0);
dydtheta = (y1-y0)/(theta1-theta0);
dxdV = (x1-x0)/(V1-V0);
dydV = (y1-y0)/(V1-V0);
f=[x1;y1];
J = [dxdtheta,dxdV;dydtheta,dydV];
t=Jf;
disp(‘ theta V f t’)
disp([theta1 norm(V1) norm(f) norm(t)])
theta0=theta1; V0=V1; theta1=theta1-t; V1=V1-t(2); it=it+1;
end
if it<maxit
theta=theta1; V=V1;
else
disp(‘Ingen konvergens!’)
theta=[];
endWhen I tried to solve theta and V with Newton for systems I got this error message
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.765187e-24.
Previously I had no problems just solving theta with Newtons for systems, but adding V got me an ill conditioned matrix. We tried different initial values to see if they were triggering, but all of them lead to the same error message. We would be very grateful for any help we could get!
function [theta,V]= newtonfsys1(theta1,V1)
t=1; it=0; maxit=100;theta0=0;V0=200/3.6;
while norm(t)>1e-9 & it<maxit
%Creates a list of x and y values
[v1,v2,v3,v4,v5]=varden(theta0,V0);
[x0,y0]=rungekutta(v1,v2,v3,v4,v5);
[v1,v2,v3,v4,v5]=varden(theta1,V1);
[x1,y1]=rungekutta(v1,v2,v3,v4,v5);
%checking if condition is being met
for i=1:length(x1)
if (abs(11.8872-x1(i))<0.01) && (abs(18.288-x1(end))<0.01)
break
end
end
for p=1:length(x0)
if (abs(11.8872-x0(p))<0.01) && (abs(18.288-x0(end))<0.01)
break
end
end
% takes the "i" & "p" from the condition and picks a good(hopefully constant for x and y
y1=y1(i)-1.001; y0=y0(p)-1.001; x1=x1(i)-11.8872; x0=x0(p)-11.8872;
%approximate derivative
dxdtheta= (x1-x0)/(theta1-theta0);
dydtheta = (y1-y0)/(theta1-theta0);
dxdV = (x1-x0)/(V1-V0);
dydV = (y1-y0)/(V1-V0);
f=[x1;y1];
J = [dxdtheta,dxdV;dydtheta,dydV];
t=Jf;
disp(‘ theta V f t’)
disp([theta1 norm(V1) norm(f) norm(t)])
theta0=theta1; V0=V1; theta1=theta1-t; V1=V1-t(2); it=it+1;
end
if it<maxit
theta=theta1; V=V1;
else
disp(‘Ingen konvergens!’)
theta=[];
end When I tried to solve theta and V with Newton for systems I got this error message
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.765187e-24.
Previously I had no problems just solving theta with Newtons for systems, but adding V got me an ill conditioned matrix. We tried different initial values to see if they were triggering, but all of them lead to the same error message. We would be very grateful for any help we could get!
function [theta,V]= newtonfsys1(theta1,V1)
t=1; it=0; maxit=100;theta0=0;V0=200/3.6;
while norm(t)>1e-9 & it<maxit
%Creates a list of x and y values
[v1,v2,v3,v4,v5]=varden(theta0,V0);
[x0,y0]=rungekutta(v1,v2,v3,v4,v5);
[v1,v2,v3,v4,v5]=varden(theta1,V1);
[x1,y1]=rungekutta(v1,v2,v3,v4,v5);
%checking if condition is being met
for i=1:length(x1)
if (abs(11.8872-x1(i))<0.01) && (abs(18.288-x1(end))<0.01)
break
end
end
for p=1:length(x0)
if (abs(11.8872-x0(p))<0.01) && (abs(18.288-x0(end))<0.01)
break
end
end
% takes the "i" & "p" from the condition and picks a good(hopefully constant for x and y
y1=y1(i)-1.001; y0=y0(p)-1.001; x1=x1(i)-11.8872; x0=x0(p)-11.8872;
%approximate derivative
dxdtheta= (x1-x0)/(theta1-theta0);
dydtheta = (y1-y0)/(theta1-theta0);
dxdV = (x1-x0)/(V1-V0);
dydV = (y1-y0)/(V1-V0);
f=[x1;y1];
J = [dxdtheta,dxdV;dydtheta,dydV];
t=Jf;
disp(‘ theta V f t’)
disp([theta1 norm(V1) norm(f) norm(t)])
theta0=theta1; V0=V1; theta1=theta1-t; V1=V1-t(2); it=it+1;
end
if it<maxit
theta=theta1; V=V1;
else
disp(‘Ingen konvergens!’)
theta=[];
end newton, matrix, singular, system, matlab MATLAB Answers — New Questions