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From: "qi li" <liqi3837671@hotmail.com>
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Subject: solving equation of multiple exponent terms summation with variable 'z'
Date: Sun, 4 Mar 2012 11:59:15 +0000 (UTC)
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Hi everyone, 
    I have a problem and I cann't figure it out. the origin is from tempting to plot a 3-d deformation sphere in SVM, it needs solve 
                              sigma(K(x,ai))=1
where K is gaussian kernel trick,which means K(x,ai)=exp(||ai-x||^2/(-2)),ai is 3 components vector,when i=1,2,3 a(:,1)=[1;1;1] a(:,2)=[2;2;2] a(:,3)=[3;3;3],  x is  [1;1;z] vector,z is varable ,so equation becomes 
         for i=1:3 
          s=s+exp(((1-a(1,i))^2+(1-a(2,i))^2+(z-a(3,i))^2)/(-2))
         end 
 then next equation s-1=0 shoulde be figured out with 'z', who has the idea how to solve it? I found using fzero() may works,but if I have no idea about the initial value(I want all possible results of the equation) and in fact there may be hundreds of equations need to be solved(I make some simplications!). 

        can someone help me? thanks advance