Expert: Sherman D. - 5/10/2004

Question
 
Dear Sir,

I am 26 yeras old Masters student of Tokyo University of Marine Sciences and Technnology.

For the last one months I am struggling to find material either from internet or library for my thesis work.

I have one set of discrete  data (t1,x1),(t2,x2)........................(tr,xr). I want to use orthogonal funcitons (fourier, chebyshev, legender) and want to estimated truncated series of each orthogonal functions. I obtained alogortham for fourier series. But I could not find for other orthogonal polynomials.

like

f(t)=a1*T0(t)+a2*T1(t)..................................+a50*Tk(t)
for chebyshev and
f(t)=a1*L0(t)+a2*L1(t)+----------------------------------+a50*Lk(t) for legendre
etc.

I request you to kindly suggest me where can I can information to use data points for truncated series of 50 terms.

Also if I use two matrices like
{X}={ a1, a2................a50}
and
{T}={T0,T1,...................Tk}

Integrate from zero to to t ({x}(transpose{T}))dt= [P]{T}, where P is operational matraix of 50x50

I request you to kinldy suggest how to find the operational matrix P

I am really struggling and spending late nights to find these procedures. I requesting you to kinldy suggest me out of this strom

With regards  

Answer
try this site.

http://mathworld.wolfram.com/OrthogonalFunctions.html

or

http://is1.websearch.com/_1_25RST530RNMHZU__websrch.barweb.3/dog/results?otmpl=d...

also try www.quickmath.com for help.