Optimal discretization and expansion order of arbitrary databy laxsu19 Tags: data set, functional expansion 

#1
Feb813, 10:31 AM

P: 14

Hi all,
I am trying to figure out 1) What to call my problem so I can better research the literature, and 2) see if anyone here knows of a solution. Essentially, I have a large set of f(x) vs x points (~20,000) which I need to split in to subdomains in x, and within each subdomain calculate a functional expansion of f(x). I want to do this in an optimal manner such that 1) the number of subdomains is minimized  or at least manageable, and 2) the number of expansion orders (probably Legendre) within each subdomain is also minimized. Does anyone have any idea what 'field' of math this could be considered, and where to begin searching around? Unfortunately, this is just a minor step in what I have to do so I don't want to expend much effort here. Thanks for your help! 



#2
Feb813, 11:46 AM

Sci Advisor
P: 3,178

Does your data contain "noise" or is the data simply known values of some precisely defined function? If your data is known values of a precisely defined function, then the general topic to research is "function approximation". For many functions, the simplest approximations (for a given mean square error) are done by using ratios of polynomials. That topic is "approximation by rational functions".




#3
Feb813, 01:09 PM

Engineering
Sci Advisor
HW Helper
Thanks
P: 6,388

If you can fit each subdomain by a low order polynomial, some buzzwords are automatic knot placement for spline curve fitting. (The "knots" are the points at the end of each subdomain, i.e. the end of each spline segment).



Register to reply 
Related Discussions  
How to find an optimal min/max combination in arbitrary set of 2tuples  Calculus  0  
expansion of an arbitrary function with Bessel functions  Calculus & Beyond Homework  0  
MATLAB: Findig period of arbitrary function given a vecor of approximated data  Engineering, Comp Sci, & Technology Homework  4  
Finite Difference Discretization of a Fourth Order Partial Differential Term  Differential Equations  4  
Optimal order to persue undergraduate upper division physics coursework  Academic Guidance  2 