Dynamics of Algorithms

The articles collected in this volume represent the contributions presented at the IMA workshop on "Dynamics of Algorithms" which took place in November 1997. The workshop was an integral part of the 1997 -98 IMA program on "Emerging Applications of Dynamical Systems." The interaction between algorithms and dynamical systems is mutually beneficial since dynamical methods can be used to study algorithms that are applied repeatedly. Convergence, asymptotic rates are indeed dynamical properties. On the other hand, the study of dynamical systems benefits enormously from having efficient algorithms to compute dynamical objects. TOC:Foreword.- Preface.- Complexity and applications of parametric algorithms of computational algebraic geometry.- Conservative and approximately conservative algorithms on manifolds.- DAEs that should not be solved.- Continuous orthonormalization for linear two-point boundary value problems revisited.- Asymptotic expansions and backward analysis for numerical integrators.- Convergence proofs for numerical IVP software.- Bifurcations of the complex Henon map.- List of Participants.