**I converted this comment into a question** since it was unrelated to the question in which it was put.

That way also other MaplePrimes users can have a shot at this new question.

Preben Alsholm

Dear Preben Alsholm

Hi;

Hope you to be healthy and have nice times,

I have another problem and if it doesn't consuming your valuable times, please guide me.

I have some Basis function,say W1(t),W2(t),W3(t),W4(t) which are orthonormal and i want to write a program that can approximate the integral of W(t)=[W1(t),W2(t),W3(t),W4(t)] again by Wi's, in other word

int(W(t')dt',t'=0..t)≈PW(t), where P is knows as integral operational matrix. the following is my attempt and unfortunately has no real solution!!!!

restart:

> # Definition of 3th B-Spline

>

> piecewise(x>=0 and x<=1,1,0):

> h[1]:=unapply(%,x):

>

> # Definition of 3th B-Spline

>

> h[2]:=simplify(int(h[1](x-t),t=0..1)):

> hh:=unapply(%,x):

>

> #Definition of 3th B-Spline

int(hh(x-t),t=0..1):

> simplify(%):

> N:=unapply(%,x):

>

> J:=1: # Number of base function is 2^J+2

> phi:=linalg[matrix](2^J+2,1):

> for i from -2 to 2^J-1

> do

> N(2^J*x-i)*h[1](x): #for deleting out side of[0,1]

> simplify(%):

> phi[i+3,1]:=unapply(%,x):

> od:

>

> w[1]:=phi[1,1](x):

> w[1]/sqrt(int(w[1]^2,x=0..1)):

> W[1]:=unapply(%,x):

>

> for i from 2 to 2^J+2

> do

> kk:=0:

> for j1 from 1 to i-1

> do

> aa[j1]:=int(phi[i,1](x)*w[j1],x=0..1):

> bb[j1]:=int(w[j1]^2,x=0..1):

> kk:=kk+aa[j1]/bb[j1]*w[j1]:

> od:

> w[i]:=simplify(phi[i,1](x)-kk):

> w[i]/sqrt(int(w[i]^2,x=0..1)):

> W[i]:=unapply(%,x): #Orthonormality process

>

>

> for j from 1 to 2^J+2 do

> for io from 1 to 2^J+2 do

> f[j]:=int(W[j](s),s=0..x);

> c[io][j]:=int(f[j](x)*W[io](x),x=0..1);

> od;

> od;

Best Wishes