Question

(a) State one advantage of Newton interpolation over the Vandermonde matrix method, and one advantage of...

(a) State one advantage of Newton interpolation over the Vandermonde matrix method, and one advantage of Lagrange interpolation over Newton interpolation.

(b) Is Bisection search a fixed point method? Justify your answer.

(c) Give two reasons why the triangular matrix method for Newton interpolation might be preferable over the Vandermonde matrix method.

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Answer #1

a) The advantage of the newton interpolation method over vandermonde matrix method is its non-reliance on matrix inversion (which can fail due to vanishing determinants).

The Lagrange approach amounts to diagonalizing the problem of finding the coefficients, so it takes only linear time to find the coefficients. This is good if you need to use the same set of points repeatedly when comared to newton interpolation

b) The Bisection Method looks to find the value c for which the plot of the function f crosses the x-axis. The c value is in this case is an approximation of the root of the function f (x). How close the value of c gets to the real root depends on the value of the tolerance we set for the algorithm.

c) 1)It give accurate value by using triangular matrix method

2)It is simple or easy to implement therotically and also practical understanding

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