Let the values of a function y = f (x) be given at different x values; thus,
Then interpolation means to find an approximate value of f (x) for an x between two x-values in (x0, xn). This is done by finding a polynomial called an interpolating polynomial which agrees with the function at the nodal points xi (i = 0, 1, 2, ⋯, n). In finding a suitable interpolating polynomial we need to have a formula for errors in polynomial approximation.
6.1.1 Formula for Errors in Polynomial Interpolation
Let y = f (x) be a function defined at the (n + 1) points
Suppose f (x) is continuous and differentiable ...