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Math 151a homework problems focusing on lagrange interpolation, constructing interpolating polynomials, neville's method, and finding error bounds for approximating functions such as sin(x) using given points.
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Math 151A Homework #4 – due Friday 10/
1 Construct a Lagrange interpolating polynomial approximation to the function f (x) = 2 x^2 − 2 using the points
a. x 0 = 0, x 1 = 1
b. x 0 = 0, x 1 = 1, x 2 = 2
c. x 0 = −1, x 1 = 0, x 2 = 1, x 3 = 2
2 Approximate
2 using Neville’s method with f (x) =
x and x 0 = 0, x 1 = 1,x 2 = 4,x 3 = 9 and x 4 = 16.
3 Find an error bound for approximating f (x) = sin(x) on the interval [0, π] with xi = iπ/ 2 for i = 0, 1 , 2.
