(a) Consider the problem of cubic polynomial interpolation p(xi) = yi , i = 0, 1

Question

(a) Consider the problem of cubic polynomial interpolation p(xi) = yi , i = 0, 1, 2, 3 with deg(p)?3 and x0, x1, x2, x3 distinct. Convert the problem of finding p(x) to another problem involving the solution of a system of linear equations. Hint: Write p(x) =a0 + a1x + a2x^2 + a3x^3 and determine a0, a1, a2, and a3. Use interpolation conditions to obtain equations involving a0,...,a3. (b) Expressing the system from (a) in the form Ax=b, identify the matrix A and the vectors b and x. Any help would be greatly appreciated.

Explanation / Answer

We can solve this problem by the following steps take p(xi) =a0 + a1x + a2x^2 + a3x^3...... where p(xi) = yi , i = 0, 1, 2, 3 now we can determine the a0, a1, a2, and a3 for each of them

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