ACETAF

A C++ Program for the
Automatic Computation of Estimates for Taylor Coefficients of Analytic Functions

Introduction

ACETAF is a program for the validated computation of bounds for Taylor coefficients and for Taylor remainder series of analytic functions. It is distributed under the terms of the GNU general public license.

The theory behind ACETAF

The mathematical foundations of ACETAF are discussed in the following papers:

	I. Eble and M. Neher: ACETAF: A Software Package for Computing Validated Bounds for Taylor Coefficients of Analytic Functions. ACM TOMS 29 (2003), 263-286.
	M. Neher: Improved validated bounds for Taylor coefficients and for Taylor remainder series. J. Comput. Appl. Math. 152 (2003), 393-404.
	M. Neher: Validated bounds for Taylor coefficients of analytic functions. Reliable Computing 7 (2001), 307-319.

ACETAF History

080918	ACETAF 3.0.1:	Compatibility update for gcc 4.2.1 and C-XSC 2.2.3. Since filib++ has undergone major revision, CoStLy now only works with C-XSC. Inclusion functions are now imported from the CoStLy 2.0.5 library. ACETAF procedures remain unchanged.
040930	ACETAF 3.0.0:	Inclusion functions are now imported from the newly developed CoStLy 1.0.0 library (improved accuracy, bug fixes). ACETAF procedures remain unchanged.
040601	ACETAF 2.8-3:	ACETAF 2.8 Build 3. Tested for SuSE Linux 9.0. Practically unchanged compared to ACETAF 2.8.
030715	ACETAF 2.8:	Adapted to GNU C++ compiler gcc 3.3 (gcc 2.95 through gcc 3.2 also work). Adapted to QT 3.0 library (QT 2.0 also works). Tested for SuSE Linux 8.2. Compiler optimization for filib++ version allowed. Improved string evaluation subroutine for validated input of constants in the scientific number format.
030314	ACETAF 2.8 preview:	Major code revision to simplify alternate use of C-XSC or filib++. Adapted to GNU C++ compiler gcc 3.2 (gcc 2.95 still works). Bug fix in Taylor remainder series. User defined order of the Taylor polynomials in methods II and IV on user defined grids allowed.
020820	ACETAF 2.718:	Improved syntax check of function expressions. Constants in scientific number format allowed.
020517	ACETAF 2.71:	First filib++ based version (faster than C-XSC based version). Minor bug fixes.
011129	ACETAF 2.7:	Computation of Taylor remainder series included. General code optimization.
010823	ACETAF 2.1:	Order of Taylor polynomials in methods II and IV optimized.
010510	ACETAF 2.0:	Mean value form included in branch and bound algorithm.
001105	ACETAF 1.0:	GUI included.
000222	ACETAF 0.1:	First release.

ACETAF Download

There's a README file for the installation. ACETAF 3.0.1 has been implemented and tested on PCs with Linux. The program requires the GNU C++ compiler gcc 4.2.1 (or higher; earlier versions from 2.95.2 may also work), the QT library 3.0 or higher, and and the C-XSC interval library (Release 2.2.3 or higher). C-XSC is available at http://www.xsc.de.

ACETAF Download

• ACETAF 3.0.1 for C-XSC (released 080918)

  What we understand by validated computation is expressed in our mission statement.

Markus Neher's homepage.