I'm very new to Mathematica. I have been having the most difficult fitting my data to a Prony series to obtain coefficients. My data is listed as:
data ={{-7.41908,0.202581},
{-7.08513,0.22534},
{-6.80688,0.263415 },
{-6.75203,0.27437 },
{-6.47366,0.352769 },
{-6.41908,0.372474 },
{-6.14086,0.521425 },
{ -6.13608,0.507203 },
{ -6.08513,0.537803 },
{ -5.80688,0.732571 },
{ -5.8041,0.713165 },
{ -5.75203,0.753371 },
{ -5.47366,0.999272 },
{ -5.4698,0.978897 },
{ -5.41908,1.03047 },
{ -5.14086,1.35962 },
{ -5.13608,1.3339 },
{ -5.08513,1.40366 },
{ -4.80688,1.85884 },
{ -4.8041,1.82376 },
{ -4.75203,1.92504 },
{ -4.47366,2.57341 },
{ -4.4698,2.56778 },
{ -4.41908,2.67567 },
{ -4.36051,2.85621 },
{ -4.14086,3.53946 },
{ -4.13608,3.53409 },
{ -4.08513,3.67948 },
{ -4.02733,3.90283 },
{ -3.80726,4.77778 },
{ -3.80281,4.77227 },
{ -3.75189,4.96328 },
{ -3.69424,5.25015 },
{ -3.47393,6.38345 },
{ -3.46948,6.36833 },
{ -3.41855,6.58298 },
{ -3.36091,6.93619 },
{ -3.1406,8.17887 },
{ -3.13614,8.14628 },
{ -3.02757,8.90897 },
{ -2.80726,10.9395 },
{ -2.80649,10.8011 },
{ -2.80281,10.7765 },
{ -2.69424,11.7196 },
{ -2.47313,13.718 },
{ -2.46948,13.6073 },
{ -2.36091,14.8401 },
{ -2.13981,17.9584 },
{ -2.13614,17.8678 },
{ -2.02757,19.8201 },
{ -1.80648,25.1663 },
{ -1.69424,28.8535 },
{ -1.57108,34.0035 },
{ -1.47315,39.0339 },
{ -1.36091,46.0734 },
{ -1.23773,55.7655 },
{ -1.13981,65.2136 },
{ -1.02757,78.5576 },
{ -0.90441,96.9397 },
{ -0.80648,114.854 },
{ -0.69424,140.088 },
{ -0.57108,174.772 },
{ -0.47315,208.272 },
{ -0.36091,254.819 },
{ -0.23774,317.221 },
{ -0.20832,328.147 },
{ -0.13981,366.807 },
{ 0.095588,528.616 },
{ 0.125032,538.08 },
{ 0.19352,592.818 },
{ 0.428922,817.148 },
{ 0.458354,823.643 },
{ 0.526852,895.643 },
{ 0.762255, 1176.53 },
{ 0.791684, 1189.2 },
{ 0.860185, 1283.84 },
{ 1.095588, 1668.42 },
{ 1.125019, 1704.64 },
{ 1.19352, 1836.48 },
{ 1.221943, 1830.4 },
{ 1.226187, 1847.67 },
{ 1.428922, 1964.63 },
{ 1.458352, 1976.94 },
{ 1.555295, 2005.88 },
{ 1.55954, 2017.68 },
{ 1.762255, 2063.7 },
{ 1.791684, 2071.22 },
{ 1.888617, 2090.3 },
{ 1.892861, 2093.55 },
{ 2.095588, 2138.75 },
{ 2.125019, 2146.72 },
{ 2.221949, 2171.14 },
{ 2.226192, 2174.12 },
{ 2.428922, 2237.78 },
{ 2.458351, 2248.93 },
{ 2.555283 , 2282.36 },
{ 2.559527 , 2285.98 },
{ 2.791685 , 2377.96 },
{ 2.888616 , 2407.15 },
{ 2.892861 , 2406.96 },
{ 3.125019 , 2492.99 },
{ 3.221949 , 2504.64 },
{ 3.226192 , 2504.83 },
{ 3.458351 , 2537.75 },
{ 3.555282 , 2527.52 },
{ 3.559526 , 2528.78 },
{ 3.791685 , 2494.84 },
{ 3.888615 , 2473.19 },
{ 3.89286 , 2471.26 },
{ 4.221949 , 2364.14 },
{ 4.226192 , 2359.41 },
{ 4.555282 , 2206.02 },
{ 4.559526 , 2193.85 },
{ 4.888615 , 1960.51 },
{ 4.89286 , 1956.46 },
{ 5.221949 , 1483.65 },
{ 5.226192 , 1474.91 }}
My prony series is listed as:
func=Normal [Series[((p_i^2)*E_i*(w^2))/(1+((p_i^2)*(w^2))),{w,0,22}]];
my fit is
FindFit[data,func,{E_i,p_i},w]
The results never fit the data.
I am very new to this and I am in great need of some assistance. I sure that the solution may be simple.
Thanks ahead of time.
