Question

Write Lagrange’s interpolation formula for unequal intervals.

Answer 1

Answer:

This formula is mainly used for unequal intervals of independent variables, although it is also used for equal intervals. However, here I write the formula for unequal intervals.

Let the values of independent variable X be a, b, c and so on and the corresponding functions are f(a), f(b), f(c) and so on. For a variable X0, the function is f(X0), and the value is given be

f(X0) = [(X0 - a) (X0 - b) (X0 - c)/ (a-b) (a-c) (a-d)] f(a) + [(X0 -a) (X0-c) (X0-d)/(b-b) (b-c) (b-d)] f(b) + ............................... and so on.