Best “ordering” for floating-point addition
ACM Transactions on Mathematical Software (TOMS)
The accuracy of floating point summation
SIAM Journal on Scientific Computing
A stochastic arithmetic for reliable scientific computation
Mathematics and Computers in Simulation
On properties of floating point arithmetics: numerical stability and the cost of accurate computations
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Pracniques: further remarks on reducing truncation errors
Communications of the ACM
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
An updated set of basic linear algebra subprograms (BLAS)
ACM Transactions on Mathematical Software (TOMS)
Design, implementation and testing of extended and mixed precision BLAS
ACM Transactions on Mathematical Software (TOMS)
Automatic differentiation of algorithms: from simulation to optimization
Automatic differentiation of algorithms: from simulation to optimization
Computer Arithmetic in Theory and Practice
Computer Arithmetic in Theory and Practice
Additive symmetries: the non-negative case
Theoretical Computer Science - Real numbers and computers
Algorithms for Quad-Double Precision Floating Point Arithmetic
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
Accurate Floating Point Summation
Accurate Floating Point Summation
Numerical Methods
What every agent-based modeller should know about floating point arithmetic
Environmental Modelling & Software
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Several different techniques and software intend to improve the accuracy of results computed in a fixed finite precision. Here we focus on the CENA method that processes an automatic correction of the first-order effect of the rounding errors the computation generates. This method provides a corrected result and a bound of the residual error for a class of algorithms we identify. We present the main features of the CENA method and illustrate its interests and limitations with examples.