Write a C program to implement the Lagrange interpolation
.
Algorithm:
Step 1. Read x, n Step 2. for i = 1 to (n + 1) is steps of 1 do Read xi,fi end for {the above statements reads x,s and the corresponding values of f is} Step 3. Sum = 0 Step 4. for i = 1 to (n + 1) in steps of 1 do Step 5. Profvnc = 1 Step 6. for J = 1 to (n + 1) in steps of 1 do Step 7. If (j ≠ i) then prodfunc = prodfunc X(x  xj) / (xi  xj) end for Step 8. Sum = Sum + fi x Prodfunc {sum is the value of f at x} end for Step 9. Write x, sum Step 10. Stop
Flowchart:
Program:
#include<stdio.h> #include<math.h> main() { float y, x[20], f[20], sum, pf; int I, j, n; printf(“enter the value of n”); scanf(“%d”, &n); printf(“enter the value to be found”); scanf(“%f”, &y); printf(“enter the values of xi’s & fi’s”); for(i = 0; i < n; i++) { pf = 1; for(j = 0; j < n; j++) { if(j != i) Pf *= (y  x[j])/(x[i] – x[j]); } sum += f[i] * pf; } printf(“\nx = %f ”, y); printf(“\n sum =%f ”, sum); }
Input & Output:
enter the value of n 4
enter the value to be found 2.5
enter the values for xi’s & fi’s
1 1
2 8
3 27
4 64
X = 2.500000
sum = 15.625000

UpdatedOct 21, 2014

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