How interpolation differs from regression? Write down algorithm and program for Lagrange interpolation.

Question

Suresh Chand · Accepted Answer

Difference between regression and interpolation: In interpolation, We are given with some data points, and we are supposed to find a curve which fits the input/output relationship perfectly. In case of interpolation, We don't have to worry about variance of the fitted curve. When we do regression, We look for a function that minimizes some cost, usually sum of squares of errors. We don't require the function to have the exact values at given points. We just a good approximation. Algorithm for Lagrange Interpolation 1. Start 2. Read number of points, say n 3. Read the value at which value is needed, say x 4. Read given data points 5. calculate values of Li as below for i = 1 to n for j = 1 to n if(j != i) L[i] = L[i] * ((x - x[j]) / (x[i]-x[j])) End if End for End for 6. Calculae interpolated value at x as below For i = 1 to n v = v + fx[i] * Lx[i] End for 7. Print the interpolated value of v at x 8. End Program: #include<stdio.h> int main(){ int n,i,j; float x, l, v=0, ax[10], fx[10], L[10]; printf('Enter the number of pointsn'); scanf('%d', &n); printf('Enter the value of x n'); scanf('%f', &x); for(i = 0; i<n; i++){ printf('Enter the value of x and fx at i = %dn', i); scanf('%f%f', &ax[i], &fx[i]); } for(i = 0; i < n; i++){ l = 1.0; for(j = 0; j < n; j++){ if( j != i ){ l = l * ((x - ax[j]) / (ax[i] - ax[j])); } } L[i] = l; } for(i = 0; i<n; i++){ v = v + fx[i] * L[i]; } printf('Interpolated value = %f', v); return 0; }

How interpolation differs from regression? Write down algorithm and program for Lagrange interpolation.

Leave your Answer:

Hits Counter

Question

How interpolation differs from regression? Write down algorithm and program for Lagrange interpolation.

Leave your Answer: