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Trying values other than random integers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg85629] Trying values other than random integers
  • From: shama shahbaz <shammashahbaz at yahoo.com>
  • Date: Sat, 16 Feb 2008 03:28:28 -0500 (EST)

Dear All
  MY problem is actually 

  i have a matrix 
             a1*x1 +a2*x2 +a3*x3  +a4*x4   +a5*x5  +a6*x6=0 
           b1*x1 +b2*x2 +b3*x3  +b4*x4   +b5*x5  +b6*x6=0 
           c1*x1 +c2*x2 +c3*x3  +c4*x4   +c5*x5  +c6*x6=0 
  where a1..a6 and b1....b6, c1...c6 are all known and x1 x2...x6 are 
all unknowns .....my problems is more like an undetermined linear 
equations but i have some constraints to the solutions of the 
x1......x6 
  1)all the x1 ....x6 must be positive and non zero 
2)x1^2 +x2^2........+x6^2=6 

is actually 
  i have a matrix 
             a1*x1 +a2*x2 +a3*x3  +a4*x4   +a5*x5  +a6*x6=0 
           b1*x1 +b2*x2 +b3*x3  +b4*x4   +b5*x5  +b6*x6=0 
           c1*x1 +c2*x2 +c3*x3  +c4*x4   +c5*x5  +c6*x6=0 
  where a1..a6 and b1....b6, c1...c6 are all known and x1 x2...x6 are 
all unknowns .....my problems is more like an undetermined linear 
equations but i have some constraints to the solutions of the 
x1......x6 
  1)all the x1 ....x6 must be positive and non zero 
2)x1^2 +x2^2........+x6^2=6 

   
   
  i was responsed by Sir Daniel to try to solve this problem like
  In[21]:= coeffs = RandomInteger[{-10,10}, {3,6}]
Out[21]= {{4, 5, -5, -4, 5, -7}, {-1, 3, -1, -4, 4, 2},
   {-9, 3, 10, -1, -2, 8}}

vars = Array[x,6];
eqns = Map[#==0&, Join[coeffs.vars, {vars.vars-6}]];
ineqs = Map[#>0&, vars];

In[25]:= InputForm[system = Join[eqns, ineqs]]
Out[25]//InputForm=
{4*x[1] + 5*x[2] - 5*x[3] - 4*x[4] + 5*x[5] - 7*x[6] == 0,
  -x[1] + 3*x[2] - x[3] - 4*x[4] + 4*x[5] + 2*x[6] == 0,
  -9*x[1] + 3*x[2] + 10*x[3] - x[4] - 2*x[5] + 8*x[6] == 0,
  -6 + x[1]^2 + x[2]^2 + x[3]^2 + x[4]^2 + x[5]^2 + x[6]^2 == 0,
  x[1] > 0, x[2] > 0, x[3] > 0, x[4] > 0, x[5] > 0, x[6] > 0}

In[30]:= InputForm[soln = Simplify[FindInstance[system, vars]]]
Out[30]//InputForm=
{{x[1] -> (-15179 + 562*Sqrt[3517202])/533792,
   x[2] -> (-30679 + 71*Sqrt[3517202])/266896,
   x[3] -> (87391 + 292*Sqrt[3517202])/533792,
   x[4] -> 7/32, x[5] -> 3/8,
   x[6] -> (-38667 + 214*Sqrt[3517202])/533792}}
   
   
  MY problem still remains when i try to use the matrix
  {{-0.2162,0.1283,-0.09057,0.07089},{0.1283,-0.09057,0.07089,-0.05793},{-0.09057,0.07089,-0.05793,0.04855}}
   
   
   
  it gives me no solution however i know that solution exsists .......can anyone help me ,should i go for non linear programming ,but it stills doesnt gaurantee me a feasible solution ...what should i do
   
   
  THnax


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