GRAM-SCHMIDT FUNCTION IS NOT GIVING CORRECT VALUES

Hello everyone,

I am trying to obtain equations of phi. I am getting wrong value of phi{3}. There is somthing wrong, which I am unable to figure out.

here is code:

clc
clear all;
initial_function=@(x,y)x.^2;
m=3;
for i=1:m;
r=floor(sqrt(i-1));
t=i-1-r.^2;
    if t/2==0;
        s=t/2;
        fm{i}=@(x,y)(x.^r).*(y.^s)
   
    else
        s=(t-1)/2;
        
        fm{i}=@(x,y)(x.^s).*(y.^r);
    end
end        
for i=1:1
phi{i}=@(x,y)fm{1}(x,y).*initial_function(x,y);
end
 xmin=@(y) y;
 syms x y;
for i=2:m
    phi{i}=@(x,y)fm{i}(x,y).*phi{1}(x,y);

    for j=1:i-1;
     
a{i}{j} = integral2(@(y,x)fm{i}(x,y).*phi{1}(x,y).*phi{j}(x,y),0,1,xmin,1)./integral2(@(y,x)phi{j}(x,y).*phi{j}(x,y),0,1,xmin,1);
  
   phi{i}=@(x,y)phi{i}(x,y)-a{i}{j}.*phi{j}(x,y);
 

    end

  phi1{i}=phi{i}(x,y);
    
end

phi{1} and phi{2} are correct.

phi{3} which i am getting from matlab is: x^2*y - (29645651611899925216907*x^2)/81129638414606681695789005144064 - (4503599623397961*x^3)/9007199254740992

while correct phi{3} is: x^2*y- 3.328*10^(-3) - 0.504x^3.

I shall be very thankful if somone can help.

Answer 1

[Scott MacKenzie]

It would be helpful if you posted your code as MATLAB code, not question text.

[Scott MacKenzie]

You could have just done this in your original question: select the code and click the code button.

Not to worry. I just tried to execute the code, but it requires the Symbolic Math Toolbox, which I don't have. Hopefully, someone else will weight in and assist. Good luck.

[nikhil mahar]

these are the functions(phi) which i am trying to get from first 2 formule.