approximation

How could one approximate Inverse Incomplete gamma function Г(s,x) by some simple analytical function f(s,Г)? That means write something like x = f(s,Г) = 12*log(123.45*Г) + Г + 123.4^s . (I need at least ideas or references.) You can look at the code in Boost: http://www.boost.org/doc/libs/1_35_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html and see what they're using. EDIT: They also have inverses: http://www.boost.org/doc/libs/1_35_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html I've found out that x = f(s,Г) with given s can be

I have a few long strings (~ 1.000.000 chars). Each string only contains symbols from the defined alphabet, for example A = {1,2,3} Sample strings string S1 = "1111111111 ..."; //[meta complexity] = 0 string S2 = "1111222333 ..."; //[meta complexity] = 10 string S3 = "1213323133 ..."; //[meta complexity] = 100 Q What kind of measures can I use to quantify the complexity of these strings? I can see that S1 is less complex than S3, but how can I do that programmatically from .NET? Any algorithm or point to the tool/literature would be greatly appreciated. Edit I tried Shannon entropy, but it

I get this code snippet from some where else. According to the webmaster, the code is picked from The art of computer programming by Knuth Since I do not have a copy of that book, may I know what is the difference among the two functions? bool approximatelyEqual(float a, float b, float epsilon) { return fabs(a - b) <= ( (fabs(a) < fabs(b) ? fabs(b) : fabs(a)) * epsilon); } bool essentiallyEqual(float a, float b, float epsilon) { return fabs(a - b) <= ( (fabs(a) > fabs(b) ? fabs(b) : fabs(a)) * epsilon); } To give an example: double a = 95.1, b = 100.0; assert( approximatelyEqual( a, b, 0.05 )

Wa are talking about Non-uniform rational B-spline . We have some simple 3 dimentional array like {1,1,1} {1,2,3} {1,3,3} {2,4,5} {2,5,6} {4,4,4} Which are points from a plane created by some B-spline How to find controll points of spline that created that plane? (I know its a hard task because of weights that need to be calculated but I really hope it is solvable) For thouse who did not got idea of question - sory my writting is wwbad - we have points that are part of plane rendered here and we need to find controll points that form a spline which solution is that rendered plane. There are

I have about hundred points, that I want to approximate with Bezier curve, but if there are more than 25 points (or something like that), factorial counting in number of combination causes number overflow. Is there a way of approximating such amount of points in a Bezier-like way (smooth curve without passing through all points, except first and last)? Or do I need to choose another approximation algorithm with the same effect? I'm using default swing drawing tools. P.S. English is not native for me, so probably I've used wrong math terms somewhere. Do you want to get one Bezier curve fitting