Reprint Server

New Applications of Taylor Model Methods

Abstract

Taylor model methods unify many concepts of high-order computational differentiation with verification approaches covering the Taylor remainder term. Not only do they provide local multivariate derivatives, they also allow for highly efficient and sharp verification. We present several recent results obtained with Taylor model methods, including verified optimization, verified quadrature and verified propagation of extended domains of initial conditions through ODEs, approaches towards verified solution of DAEs and PDEs. In all cases, the methods allow the development of new numeric-analytic tools that efficiently capitalize on the availability of derivatives and sharp inclusions over extended ranges. Applications of the methods are given, including global optimization, very high-dimensional numeric quadrature, particle accelerators, and dynamics of near-earth asteroids.

K. Makino, M. Berz, in: "Automatic Differentiation: From Simulation to Optimization", G. Corliss, C. Faure, A. Griewank, L. Hascoet, U. Naumann (Eds.) (2001) Springer

Download

Click on the icon to download the corresponding file.

Download Postscript version (397186 Bytes).
Download Adobe PDF version (220608 Bytes).

Go Back to the reprint server.
Go Back to the home page.

This page is maintained by Kyoko Makino. Please contact her if there are any problems with it.