Reprint Server

Towards a Universal Data Type for Scientific Computing


Modern scientific computing uses an abundance of data types. Besides floating point numbers, we routinely use intervals, univariate Taylor series, Taylor series with interval coefficients, and more recently multivariate Taylor series. Newer are Taylor models, which allow verified calculations like intervals, but largely avoid many of their limitations, including the cancellation effect, dimensionality curse, and low-order scaling of resulting width to domain width. Another more recent structure is the Levi-Civita numbers, which allow viewing many aspects of scientific computation as an application of arithmetic and analysis with infinitely small numbers, and which are useful for a variety of purposes including the assessment of differentiability at branch points. We propose new methods based on partially ordered Levi-Civita algebras that allow for a unification of all these various approaches into one single data type.

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


Click on the icon to download the corresponding file.

Download Adobe PDF version (206694 Bytes).
Download Postscript version (193622 Bytes).

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

This page is maintained by Ravi Jagasia. Please contact him if there are any problems with it.