## Department of Mathematics

Write and call a kernel to evaluate the matrix product $\left(\frac1{h^2}\right) \begin{bmatrix} -2 & 1 & 0 & 0 & \dots & 0\\ 1 & -2 & 1 & 0 & \dots & 0\\ 0 & 1 & -1 & 1 & \dots & 0\\ \vdots & &&& \ddots & \vdots\\ 0 & \dots & &0&1&-2\\ \end{bmatrix} u = v,$ Where $$h$$ is the distance between the uniformly spaced points of a partition on [0,1].
Recall that the matrix product represents an estimate of the second derivative of a function with values $$u_i$$ at the points $$x_i$$ of the partition. You can use this code as a starting point for your program. In that case all you need to do is fill in a few lines.