How to solve non linear equations with three variables? I tried matlab codes available in www.mathworks.in. and also I tried Newton rapson method .But I could not get proper output.Please help me to solve this.
1 view (last 30 days)
Show older comments
- ((x-x1)^2+(y-y1)^2+(z-z1)^2)^2-((x-x2)^2+(y-y2)^2+(z-z2)^2)^2=t1.
- ((x-x2)^2+(y-y2)^2+(z-z2)^2)^2-((x-x3)^2+(y-y3)^2+(z-z3)^2)^2=t2.
- ((x-x3)^2+(y-y3)^2+(z-z3)^2)^2-((x-x4)^2+(y-y4)^2+(z-z4)^2)^2=t3.Only unknowns are x,y,z.All other variables are known.
4 Comments
Walter Roberson
on 19 Dec 2012
Roger, please re-check. Possibly the equations have been edited since you first looked. The sum of the first two cancels out the terms involving x2, y2, z2, leaving the 1's minus the 3's, but that is not the same as what is in the third equation.
Roger Stafford
on 20 Dec 2012
Thank you, you're right, Walter, there has been a significant alteration in the stated problem. The third equation formerly involved the points (x1,y1,z1) and (x3,y3,z3) and the three equations were mutually dependent or incompatible, depending on the t values. I am accustomed to CSSM where no change can be entered after an article is once entered.
Nevertheless it still is not a problem in sphere intersection. Each of the loci of the three equations is a surface of revolution about the connecting line segment between the two corresponding fixed points and approaches asymptotically the plane orthogonally bisecting that segment. With a 't' value of zero it would be that plane itself. The desired solution will be the point or points of intersection of the three surfaces - not a trivial problem.
Roger Stafford
Answers (2)
Roger Stafford
on 16 Dec 2012
Edited: Walter Roberson
on 19 Dec 2012
There is a very good reason why those three equations present a difficulty. If the left sides of the first two equations are added, their sum would be identically equal to the left side of the third equation. This means that to have any solutions at all, it must be true that t1+t2=t3. If that is true, then there really are only two independent equations but still three unknowns, and in general these would then have an infinite continuum of possible solutions.
It is not a well-posed problem.
Roger Stafford
7 Comments
Roger Stafford
on 20 Dec 2012
My apologies to you, Deepak. I was unaware of the editing change that had been made to the original equations. As I pointed out to Walter, the solution to the revised equations is the point or points of intersection of three surfaces of revolution. Finding these intersection points using a function like 'fsolve' may be a matter of carefully selecting the appropriate initial estimates, and the same is true with the Newton-Raphson method. I would expect either one of them, particularly the latter, to fail unless a reasonably close initial value were used.
Roger Stafford
Muruganandham Subramanian
on 14 Dec 2012
Edited: Muruganandham Subramanian
on 14 Dec 2012
try using inline()
>>doc inline/formula
See Also
Categories
Find more on Assembly in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!