Complexity and Differential Equations

Publisher Summary This chapter focuses on three analytic complexity topics, which are the subject of active research in the Department of Computer Science of Yale University. The first topic deals with the complexity of interpolation problems. The second topic discusses the optimal storage algorithms introduced for the direct solution of sparse linear systems of equations. The chapter presents the application of these algorithms to the 5-point difference equations that arise as approximations to partial differential equations in two independent variables. This class of algorithms is a good example of the general phenomenon of being able to construct algorithms for particular problems that trade-off computing time for storage. The third topic deals with a special case of the general problem for finding fixed points.