How to solve 4 nonlinear equations (in 4 unknowns) ITERATIVELY

Hi,

Please help me in solving 4 nonlinear equations ITERATIVELY...

a1, b1, c1 d1, a2, b2, c2, d2, a3, b3, c3, d3, a4, b4, c4, d4, k1, k2, k3 all are known

   (a1-x(1))^2+(a2-x(2))^2+(a3-x(3))^2-x(4)^2=0
   (b1-x(1))^2+(b2-x(2))^2+(b3-x(3))^2-k1*(x(4))^2=0
   (c1-x(1))^2+(c2-x(2))^2+(c3-x(3))^2-k2*(x(4))^2=0
   (d1-x(1))^2+(d2-x(2))^2+(d3-x(3))^2-k3*(x(4))^2=0

*I know how to solve them using solve command to get just a single solution*

Help!

Thanks

Answer 1

[Andrei Bobrov]

variant

a = rand(4);
a(1,end) = 1;
f1 = @(x)sum(bsxfun(@minus,a(:,1:end-1),reshape(x(1:end-1),1,[])).^2,2) - a(:,end)*(x(end)^2);
x = fsolve(f1,randi(12,4,1));

[manish sharma]

Hi Andrei,

Can you please elaborate it.

I am a beginner.

Thanks for your answer.

[Andrei Bobrov]

in our case:

a = [a1 a2 a3 1

b1 b2 b3 k1

c1 c2 c3 k2

d1 d2 d3 k3]

x = [x(1);x(2);x(3);x(4)]

[manish sharma]

Thanks,

BTW I got the desired results by using Newton Raphson method for solving a sysytem of non linear equations.

Bye

Answer 2

[Nuno]

this can be applied to this I have x1,y1,z1,x2,y2,z2,x3,y3,z3,x4,y4,z4

(x0-x1)^2+(y0-y1)^2+(z0-z1)^2=r^2

(x0-x2)^2+(y0-y2)^2+(z0-z2)^2=r^2

(x0-x3)^2+(y0-y3)^2+(z0-z3)^2=r^2

(x0-x4)^2+(y0-y3)^2+(z0-z4)^2=r^2

I need to get x0,y0,z0 and r.

I applied that code and the results are very weird