Pracniques: further remarks on reducing truncation errors

@article{Kahan1965PracniquesFR,
  title={Pracniques: further remarks on reducing truncation errors},
  author={William Kahan},
  journal={Commun. ACM},
  year={1965},
  volume={8},
  pages={40}
}
  • W. Kahan
  • Published 1965
  • Computer Science
  • Commun. ACM
the symbol f'l denotes an AND operation and the symbol • denotes a multiplication operation. (2) The result of an OR operation w i t h any number of Boolean variables is the same as the (arithmetic) addition of tile x, y, z integer variables after the following t e s t is made: (a) If the sum is equal to zero, the result is correct; (b) If the sum is larger thart zero, the answer is a 1; i.e. where the symbol O denotes an OR (}peration and the symbol-{-denotes an addition operation. (3) The… 
Calculation of Scalar Isosurface Area and Applications
CALCULATION OF SCALAR ISO-SURFACE AREA AND APPLICATIONS
Error bounds on complex floating-point multiplication with an FMA
TLDR
It is proved that the term $2u$ is asymptotically optimal not only for this naive FMA-based algorithm, but also for two other algorithms, which use the FMA operation as an efficient way of implementing rounding error compensation.
MCALIB: Measuring Sensitivity to Rounding Error with Monte Carlo Programming
TLDR
This work presents an open source system that automates the quantitative analysis of floating point rounding errors through the use of C-based source-to-source compilation and a Monte Carlo arithmetic library.
Fast exact summation using small and large superaccumulators
TLDR
Two new methods for exactly summing a set of floating-point numbers, and then correctly rounding to the nearest floating-points are presented, using variations on the concept of a "superaccumulator" - a large fixed-point number that can exactly represent the sum of any reasonable number of Floating Point Values.
Accuracy and Efficiency in Fixed-Point Neural ODE Solvers
TLDR
Simulation of neural behavior on digital architectures often requires the solution of ordinary differential equations (ODEs) at each step of the simulation, and some solution methods are explored, showing how specific techniques can be used to find balanced solutions.
Exploiting Structure in Floating-Point Arithmetic
TLDR
This paper reviews some recent improvements of several classical, Wilkinson-style error bounds from linear algebra and complex arithmetic that all rely on low-level structure properties and how to exploit them in rounding error analysis.
New Trends in Databases and Information Systems
TLDR
The aim of this paper is to present such events, their motivations and topics of interest, as well as briefly outline the papers selected for presentations, and selected papers will then be included in the remainder of this volume.
Finding rare numerical stability errors in concurrent computations
TLDR
The cross-entropy method is applied -- a generic approach to rare event simulation and combinatorial optimization -- to detect rare numerical instability in concurrent programs and it is argued that its performance is superior to other techniques.
On the safety of Gomory cut generators
TLDR
An experimental setup that allows statistically significant comparisons of generators and a parameter optimization algorithm is proposed to find a Gomory mixed-integer cut generator that is as safe as a benchmark cut generator from a commercial solver even though it generates many more cuts.
...
...