Sometimes this can lead to an interpolant that is excessively wriggly, with wildly oscillating derivatives, particularly if the data is 'noisy' (contains large errors). In this assignment, we relax the requirement for (1.1) to pass exactly through the data points and instead seek a balance between that requirement and the 'smoothness' of the fitted function. Recall that we forced the spline (1.1) to pass precisely through the data points by solving the linear system Bx = f , where x = [a, b, c2, . . . , cN 1]T, f = [f1, f2, f3, . . . , fN ]T, and B = 1 x1 |x1 x2|3 |x1 xN 1|3 1 x2 |x2 x2|3 |x2 xN 1|3 1 x3 |x3 x2|3 |x3 xN 1|3 ... ... ... ... 1 xN |xN x2|3 |xN xN 1|3 , which means that the norm of the residuals Bx f = 0. In this assign- ment, we permit Bxf to be nonzero, which means the spline (1.1) will not pass precisely through the data points. The magnitude of Bx