Accurate summation, dot product and polynomial evaluation in complex floating point arithmetic

Authors:
Stef Graillat;Valérie Ménissier-Morain
Affiliations:
UPMC Univ Paris 06, UMR 7606, LIP6, 4 place Jussieu, F-75252, Paris cedex 05, France;UPMC Univ Paris 06, UMR 7606, LIP6, 4 place Jussieu, F-75252, Paris cedex 05, France
Venue:
Information and Computation
Year:
2012

Citing 8
Cited 0

The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms

The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Design, implementation and testing of extended and mixed precision BLAS

ACM Transactions on Mathematical Software (TOMS)
Accuracy and Stability of Numerical Algorithms

Accuracy and Stability of Numerical Algorithms
Scalar fused multiply-add instructions produce floating-point matrix arithmetic provably accurate to the penultimate digit

ACM Transactions on Mathematical Software (TOMS)
Accurate and Efficient Floating Point Summation

SIAM Journal on Scientific Computing
Accurate Sum and Dot Product

SIAM Journal on Scientific Computing
Some Functions Computable with a Fused-Mac

ARITH '05 Proceedings of the 17th IEEE Symposium on Computer Arithmetic
MPFR: A multiple-precision binary floating-point library with correct rounding

ACM Transactions on Mathematical Software (TOMS)

Quantified Score

Hi-index	0.00

Visualization

Abstract

Several different techniques and softwares intend to improve the accuracy of results computed in a fixed finite precision. Here we focus on methods to improve the accuracy of summation, dot product and polynomial evaluation. Such algorithms exist real floating point numbers. In this paper, we provide new algorithms which deal with complex floating point numbers. We show that the computed results are as accurate as if computed in twice the working precision. The algorithms are simple since they only require addition, subtraction and multiplication of floating point numbers in the same working precision as the given data.