Perspectives on Enclosure Methods [Paperback]

Enclosure methods and their applications have been developed to a high standard during the last decades. These methods guarantee the validity of the computed results. This means they are of the same standard as the rest of mathematics. The book deals with a wide variety of aspects of enclosure methods. All contributions follow the common goal to push the limits of enclosure methods forward. Topics that are treated include basic questions of arithmetic, proving conjectures, bounds for Krylow type linear system solvers, bounds for eigenvalues, the wrapping effect, algorithmic differencing, differential equations, finite element methods, application in robotics, and nonsmooth global optimization.Enclosure methods and their applications have been developed to a high standard during the last decades. These methods guarantee the validity of the computed results. This means they are of the same standard as the rest of mathematics. The book deals with a wide variety of aspects of enclosure methods. All contributions follow the common goal to push the limits of enclosure methods forward. Topics that are treated include basic questions of arithmetic, proving conjectures, bounds for Krylow type linear system solvers, bounds for eigenvalues, the wrapping effect, algorithmic differencing, differential equations, finite element methods, application in robotics, and nonsmooth global optimization.Proving Conjectures by Use of Interval Arithmetic.- 1 Computer Assisted Proofs in Analysis.- 2 The Kepler Conjecture.- 3 The Double Bubble Conjecture.- 4 The Dirac-Schwinger Conjecture.- 5 Chaos conjectures.- References.- Advanced Arithmetic for the Digital Computer Interval Arithmetic Revisited.- 1 Introduction and Historical Remarks.- 2 Interval Arithmetic, a Powerful Calculus to Deal with Inequalities.- 3 Interval Arithmetic as Executable Set Operations.- 4 Enclosing the Range of Function Values.- 5 The Interval Newton Method.- 6 Extended Interval Arithmetic.- 7 The Extended Interval l|