LstSquApprox.m

function [fintP,axk,Snx,Sqa_err]=LstSquApprox(f,w,n)
% 列让德多项式最佳平方逼近计算程序,

syms t

sumsf=zeros(1,n+1);sn=zeros(1,n-1);

for i=1:n+1
   Pn0=2^(-(i-1))/factorial(i-1)*(t^2-1)^(i-1);
   Pnx(i)=diff(Pn0,i-1);
   sumsf(i)=int(w*f*Pnx(i),-1,1);
   sn(i)=2/(2*(i-1)+1);
end

digits(5);
fintP=vpa(sumsf);
axk=fintP./sn;
Snx=simplify(Pnx*axk');

Sqa_err=abs(vpa(int(f*f,-1,1))-sn*axk'.^2)^0.5;