algorithm - Determinating Complexity time -

i'm doing project university how determinate complexity assuming known algorithm running times depending on data size.

the types of algorithm use polynomial (n2, n3,..,n6), logarithmic , exponential.

for example, imput of program can be:

n 1 2 3 4 5 6 7 8 9 10 11 12 (data size)

t(n) 0,9 / 1,6 / 2,3 / 3,0 / 3,7 / 4,4 / 5,1 / 5,8 / 6,5 / 7,2 / 7,9 / 8,6

so, i've got algorithm polynomial , logarithmic complexity, now, data maximum 20

polynomial:

while answer = -1 , j > 12 loop aux:= true;   k in 1..j loop     c := polynomial(k+1);     polynomial(k) := polynomial(k+1) - polynomial(k);       aux:= aux , abs(polynomial(k)) < abs (c * 0.005);  --almost equal   end loop;    if aux      aux := 19 - j;      end if;    j := j-1; end loop; 

i've reached dead end exponencial one. give me hint? thank much.

this sounds stochastic problem i.e. find best model fit given set of discrete points. first thing determine type: logarithmic/polynomial/exponential. can study discrete derivative @ each point. if value of first derivative decreasing => logarithmic. determine if polynomial or exponential again should study derivative, time not first order. following can observed: continues derivation of exponential function exponential while polynomial 1 linear (derivative close 0). hence if after couple of derivations value close 0 => polynomial.

having determined type of model fit points model. can in c++ of eigen library , their implementation of levenberg–marquardt algorithm