Question: 1. (10 marks) Compute the Lagrange interpolation polynomial for { (0, 1), (1, 2), (2, 3), (3, -2) } and express the polynomial in the

1. (10 marks) Compute the Lagrange interpolation polynomial for { (0, 1), (1, 2), (2, 3), (3, -2) } and express the polynomial in the simplest form. We compute the divided differences using the table. f [xi] f [xi, xit]] f[xi, Xi+1, xit2] f[xi, Xit1, Xit2, Xi+3) 0 1 2 O -1 2 3 -3 -5 3 -2 Taking the upper diagonal entries, Newton's divided formula simplifies to L2(x) = 1+x -x(x -1)(x -2) =1 -x+3x2 -23

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