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numerical methods, Mathematics

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Consider the following interpolation problem:

Find a quadratic polynomial p(x) such that
p(x0) = y0 p’(x1) = y’1 , p(x2) = y2

where x0 is different from x2 and y0, y’1 , y2 are the given data.

(a) What conditions must be satisfied for such a p(x) to exist and be unique?

(b) When p(x) exists, construct the basis functions Ti(x) for i = 0, 1, 2 such that

p(x) = y0*T0(x) + y’1*T1(x) + y2*T2(x).

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