Updating and downdating matrix factorizations: a change in plans

We seldom get it right the first time. Whether we´re composing an email, seasoning a stew, painting a picture, or planning an experiment, we almost always make improvements on our original thought. The same is true of engineering design; we draft a plan, but changes are almost always made. Perhaps the customer changes the performance specifications, or perhaps a substitution of building materials leads to a redesign. In this homework assignment, we consider numerical methods that make it easier to reanalyze the design after small changes are made. For definiteness, we focus on truss design, but the same principles apply to any linear model