2. An alternative approach to the method in Theorem 8.1, for constructing the interpolating polynomial, consists of dir...
2. An alternative approach to the method in Theorem 8.1, for constructing the interpolating polynomial, consists of directly enforcing the n 1 in terpolation constraints on IIn and then computing the coefficients ai. By doing so, we end up with a linear system Xa- y, with a -(ao, , an)1. у (yo, ,Yn)1, that X is nonsingular if the nodes xi are distinct and X-lx】. X is called Vandermonde matrix. Prove Π (zi-rs) by recursion on n.] Hint: show that det (X)- 0jn
2. An alternative approach to the method in Theorem 8.1, for constructing the interpolating polynomial, consists of directly enforcing the n 1 in terpolation constraints on IIn and then computing the coefficients ai. By doing so, we end up with a linear system Xa- y, with a -(ao, , an)1. у (yo, ,Yn)1, that X is nonsingular if the nodes xi are distinct and X-lx】. X is called Vandermonde matrix. Prove Π (zi-rs) by recursion on n.] Hint: show that det (X)- 0jn