Sensitivity Analysis: When a Little Means a Lot

In contrast to classroom exercises, the real world rarely presents us with a problem in which the data is known with absolute certainty. some parameters (such as n) we can define with certainty, and others (such as h) we know to high precision, but most data is measured and therefore contains measurement error. So what we really solve isn't the problem we want, but some nearby problem, and in addition to reporting the computed solution, we really need to report a bound on either * the difference between the true solution and the computed solution (a forward error bound), or * the difference between the problem we solved and the problem we wanted to solve (a backward error bound). This need occurs throughout computational science. For example, * If we compute the resonant frequencies of a model of a building, we want to know how these frequencies change if the load within the building changes. * If we compute the stresses on a bridge, we want to know how sensitive these values are to changes that might occur as the bridge ages. * If we develop a model for our data and fit the parameters using least squares, we want to know how much the parameters would change if the data were wiggled within the uncertainty limits. In this homework assignment, we use some simple problems to investigate the use of several tools for sensitivity analysis