Hello,

Curently I am trying to find the roots of the following function:

dataTable = {{1, 4.19322*10^7}, {1.10517, 4.93649*10^7}, {1.2214, 
  5.92578*10^7}, {1.34986, 7.28902*10^7}, {1.49182, 
  9.21686*10^7}, {1.64872, 1.19844*10^8}, {1.82212, 
  1.60884*10^8}, {2.01375, 2.23547*10^8}, {2.22554, 
  3.21208*10^8}, {2.4596, 4.79926*10^8}, {2.71828, 
  7.43284*10^8}, {3.00417, 1.19955*10^9}, {3.32012, 
  2.00194*10^9}, {3.6693, 3.49278*10^9}, {4.0552, 
  6.24548*10^9}, {4.48169, 1.1651*10^10}, {4.95303, 
  2.244*10^10}, {5.47395, 4.48281*10^10}, {6.04965, 
  9.1791*10^10}, {6.68589, 1.93113*10^11}, {7.38906, 
  4.20822*10^11}, {8.16617, 9.25839*10^11}, {9.02501, 
  2.0749*10^12}, {9.97418, 4.73217*10^12}, {11.0232, 
  1.09285*10^13}, {12.1825, 2.60396*10^13}, {13.4637, 
  5.9518*10^13}, {14.8797, 1.43135*10^14}, {16.4446, 
  3.41386*10^14}, {18.1741, 8.45196*10^14}, {20.0855, 
  2.02392*10^15}, {22.198, 4.76014*10^15}, {24.5325, 
  1.16761*10^16}, {27.1126, 2.79474*10^16}, {29.9641, 
  7.62706*10^16}, {33.1155, 1.68507*10^17}, {36.5982, 
  4.3599*10^17}, {40.4473, 1.10525*10^18}, {44.7012, 
  2.55076*10^18}, {49.4024, 6.02272*10^18}, {54.5982, 
  1.42872*10^19}, {60.3403, 3.88896*10^19}, {66.6863, 
  8.76079*10^19}, {73.6998, 2.21779*10^20}, {81.4509, 
  5.45498*10^20}, {90.0171, 1.43749*10^21}, {99.4843, 
  2.86785*10^21}, {109.947, 7.96947*10^21}, {121.51, 
  2.13845*10^22}, {134.29, 4.33563*10^22}}

My plan was to interpolate and then find the roots:

f = Interpolation[%];
Show[ListLogPlot[dataTable] , 
 LogPlot[f[x], {x, 1, First[Last[dataTable]]}]]
FindRoot[f[x], {x, 1 + i}]

Obviously there are only Complex Roots. I was not able to find a good starting point to find a root of the function, so I tried it using FindAllRoots.m :

RootSearch[f[x] == 0, {x, 1, 100}]

But I get:

$MinPrecision::precset: Cannot set $MinPrecision to -\[Infinity]; value must be a non-negative number or Infinity. >>

Actually I do not know what that means..

I expected it to fail since there are only examples with real roots given in the help of FindAllRoots. However.. I am not sure if I am on the right path. Do you know another way to solve the poblem? Am I doing something wrong?

Best Regards,

Marius