O/P of Lagrange Polynomial

I am writing a script for generating lagrange polynomial. I have a problem with output. please guide. why is the op looking weird.

 %%modelling a lagrange polynomial

 %%inputs to code will be node points and function value at nodes

 %%output will be polynomials p1(x), p2(x), p3(x) and p4(x)

 %%count of math operations for each polynomial

   clc

d=input('Enter degree of Langragian Polynomial: ');

n = input('Enter the node count ');

N = input('enter nodes in [] bracket:-');

Fx = input('enter function value in [] bracket:-');

   disp('Nodes:')

   disp(N);

   disp('Function values:')

   disp(Fx);

   syms x;

 s=0;

 for k=1:n;

    Poly=Fx(k);

    for j=1:n;

        if j~=k

     Poly=Poly*(x-N(j))/(N(k)-N(j));

        end

    end

    s=s+Poly;

 %      digits(4);

 %      r = vpa(s);

 %      fplot(matlabFunction(r),[min(N),max(N)]);

 %      hold on;

 %     o = i^2;

 %     O = sprintf('Mathematical Operations required for P%d(x) is %d',i,o);

 %     disp(O);

 end

 fprintf('Polynomial is \n');

 digits(4); %to restrict decimal form to 4 signi. digit

 r=vpa(s); %to represent in decimal form

disp(s);

 % figure(1);

 % fplot(matlabFunction(s),[min(N),max(N)]);

 % figure(2);

 % ezplot(s,[min(N)-3,max(N)+3]);

output

 Enter degree of Langragian Polynomial: 4
 Enter the node count 5
 enter nodes in [] bracket:-[4 5 6 7 8]
 enter function value in [] bracket:-[2 2.23607 2.44949 2.64979 2.82843]
 Nodes:
      4     5     6     7     8

 Function values:
     2.0000    2.2361    2.4495    2.6498    2.8284

 Polynomial is 
 (((3184529073510883*x)/4503599627370496 - 3184529073510883/1125899906842624)*(x - 5)*(x - 6)*(x - 7))/6 + ((2*x - 
 10)*(x - 6)*(x - 7)*(x - 8))/24 + (((2757880562811939*x)/2251799813685248 - 2757880562811939/562949953421312)*(x - 
 5)*(x - 7)*(x - 8))/2 - (((1258795502346793*x)/562949953421312 - 1258795502346793/140737488355328)*(x - 6)*(x - 7)*(x 
 - 8))/6 - ((x - 5)*(x - 6)*(x - 8)*((1988932209435011*x)/2251799813685248 - 1988932209435011/562949953421312))/2

>>

Answer 1

[nick]

Hi Shivam,

I understand from your query that you need help understanding why the displayed output of the Lagrange polynomial is in rational form rather than decimal form.

Kindly refer to the code snippet from the code you shared. To display the polynomial in decimal form, you should display “r” instead of “s”, as “s” is a symbolic expression that contains the coefficients in rational numbers.

fprintf('Polynomial is \n');

digits(4); %to restrict decimal form to 4 signi. Digit

r = vpa(s); %to represent in decimal form

disp(r); % here instead of ‘s’, as in the code shared by you, ‘r’ the decimal form should be displayed

Here is the obtained output of the code you shared:

Figure 1 Obtained Lagrange Polynomial

Hope this helps,

Regards,

Neelanshu