First Course In Numerical Methods Solution Manual -

Evaluating these expressions at x = 0.5, we get:

f(0.5) ≈ 0.375(0) - 0.25(0.8414709848079) + 0.0625(0.9092974268257) ≈ 0.479425538. First Course In Numerical Methods Solution Manual

Using Lagrange interpolation, we can write the approximate value of f(x) as: Evaluating these expressions at x = 0

L0(0.5) = 0.375, L1(0.5) = -0.25, L2(0.5) = 0.0625. where L0(x) = (x - 1)(x - 2)/((0

Use Lagrange interpolation to find an approximate value of the function f(x) = sin(x) at x = 0.5, given the data points (0, 0), (1, sin(1)), and (2, sin(2)).

where L0(x) = (x - 1)(x - 2)/((0 - 1)(0 - 2)) = (x^2 - 3x + 2)/2, L1(x) = (x - 0)(x - 2)/((1 - 0)(1 - 2)) = -(x^2 - 2x), L2(x) = (x - 0)(x - 1)/((2 - 0)(2 - 1)) = (x^2 - x)/2.

Substituting these values into the Lagrange interpolation formula, we get: