How can I solve these 3 nonlinear equations for eqn1, eqn2 and eqn3 goes to zero?

eqn1=(((((x-4157246.5346)^2)+((y-671877.0281)^2)+((z-4774581.6314)^2))^0.5)-566.8635)

eqn2=(((((x-4156749.5977)^2)+((y-672711.4554)^2)+((z-4774981.5459)^2))^0.5)-1324.2380)

eqn3=(((((x-4156748.6829)^2)+((y-671171.9385)^2)+((z-4775235.5483)^2))^0.5)-542.2609)

%my roots(x y z) should satisfy each equations for 0

[Matt J]

sermet, you should be abundantly familiar with FSOLVE by now, after these threads

http://www.mathworks.com/matlabcentral/answers/118858-how-to-use-fsolve-function

http://www.mathworks.com/matlabcentral/answers/108260-i-have-more-non-linear-equations-than-unknowns-how-can-i-solve-it-in-matlab-one-method-i-know-is-n

particularly as related to solving for intersections of spheres. I will delete this thread within 24 hours (and all future ones like it) unless you explain how it is substantively different.

[Roger Stafford]

Matt, I urge you not to delete this thread and to reopen it for discussion. My argument for this is that this particular problem does not require the use of iteration as performed by 'fsolve' and other similar optimization routines. There is a very direct and simple computation that leads to the solution, as evidenced by the thread I have referenced below. It is almost like having a solution using 'solve' except that I believe 'solve' itself would give a rather long and difficult expression as solution in this case. I don't recall ever giving this as an answer to Sermet in the past.

Answer 1

[Roger Stafford]

You are asking for the two intersections between three spheres, (that is, provided they do intersect.) I wrote up a method of finding these two intersections in the sixth article of the matlab newsreader thread at:

 http://www.mathworks.com/matlabcentral/newsreader/view_thread/318366

You are welcome to use it.