Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
C++ Toolbox for Verified Scientific Computing I: Basic Numerical Problems
C++ Toolbox for Verified Scientific Computing I: Basic Numerical Problems
Computer Arithmetic in Theory and Practice
Computer Arithmetic in Theory and Practice
C-XSC: A C++ Class Library for Extended Scientific Computing
C-XSC: A C++ Class Library for Extended Scientific Computing
Improved validated bounds for Taylor coefficients and for Taylor remainder series
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
ACM Transactions on Mathematical Software (TOMS)
The design of the Boost interval arithmetic library
Theoretical Computer Science - Real numbers and computers
FILIB++, a fast interval library supporting containment computations
ACM Transactions on Mathematical Software (TOMS)
Complex standard functions and their implementation in the CoStLy library
ACM Transactions on Mathematical Software (TOMS)
Inner and outer bounds for the solution set of parametric linear systems
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Fast (Parallel) Dense Linear System Solvers in C-XSC Using Error Free Transformations and BLAS
Numerical Validation in Current Hardware Architectures
A Modified Staggered Correction Arithmetic with Enhanced Accuracy and Very Wide Exponent Range
Numerical Validation in Current Hardware Architectures
Mathematica Connectivity to Interval Libraries filib++ and C-XSC
Numerical Validation in Current Hardware Architectures
Standardized interval arithmetic and interval arithmetic used in libraries
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Comments on fast and exact accumulation of products
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Arbitrary precision complex interval computations in C-XSC
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part II
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C-XSC is an extensive and sophisticated C++ class library for the development and implementation of self-validating numerical software. Many numerical data types of distinct precision as well as operators and functions for these data types are provided by the library. Moreover, a large number of self-verifying numerical routines are integrated, and many additional packages for the reliable solution of numerical problems have been built on the C-XSC library. An MPI extension for C-XSC data types is available, enabling the efficient implementation of C-XSC software on parallel computers. In this paper, we present the basic features of C-XSC and we show by code examples that the development of sophisticated mathematical software delivering verified numerical results is considerably simplified when using C-XSC. Some features concerning complex interval arithmetic and complex interval functions (C-XSC, CoStLy, ACETAF) are discussed in more detail. All sample codes listed in this paper are available on the web page http://www.math.uni-wuppertal.de/~xsc/cxsc/examples