Urgent Interpolation is a type of estimation, a method of constructing new data points within the range of a discrete set of known data points. The Vandermonde method is the most straight-forwardmethod which may be used to find an interpolating polynomial. The substitution of the points into the desired polynomial yields a system of linear equations in the coefficients of the polynomial.Suppose we have 3 points and we want to fit a quadratic interpolating polynomial through these points,To + r1r + r2T²We can find an interpolating polynomial that passes through 3 points(T1, Y1), (T2, Y2), (03, Y3)by solving the following matrix system.To + r1¤1+ 3r2 = Y1To + ri12 + 3r21, = Y2To + r113 + 3r2x = y3a) The coefficient matrix for this system is a Vandermonde matrix. Compute the determinant of the Vandermonde matrix.b) Suppose entries of x are (0, 1, 2), and entries of y are the last 3 digits of your student number (If last 3 digits are y1y2y3, the first entry of vector y is y1, the second entry is y2, the third entryis y3). Solve the matrix system with Cramer's Rule and obtain the interpolating polynomial.

Name: Urgent Interpolation is a type of estimation, a method of constructing
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Urgent Interpolation is a type of estimation, a method of constructing new data points within the range of a discrete set of known data points. The Vandermonde method is the most straight-forwardmethod which may be used to find an interpolating polyn