Fast high precision summation

スポンサーリンク

概要

• 論文の詳細を見る

• Given a vector pi of floating-point numbers with exact sum s, we present a new algorithm with the following property: Either the result is a faithful rounding of s, or otherwise the result has a relative error not larger than epsKcond(∑pi) for K to be specified. The statements are also true in the presence of underflow, the computing time does not depend on the exponent range, and no extra memory is required. Our algorithm is fast in terms of measured computing time because it allows good instruction-level parallelism. A special version for K=2, i.e., quadruple precision is also presented. Computational results show that this algorithm is more accurate and faster than competitors such as XBLAS.

著者

• Rump Siegfried

  Institute For Reliable Computing Hamburg University Of Technology

• Ogita Takeshi

  Waseda University, Faculty of Science and Engineering

関連論文

• 行列式の精度保証付き数値計算法
• 大規模疎行列の正定値性の保証法 (計算科学の基盤技術としての高速アルゴリズムとその周辺)
• On the generation of very ill-conditioned integer matrices
• A model problem for global optimization
• Iterative Refinement for Ill-Conditioned Linear Systems
• Adaptive and Efficient Algorithm for 2D Orientation Problem
• Inversion of Extremely Ill-Conditioned Matrices in Floating-Point
• Fast high precision summation
• Verified computation of a disc containing exactly k roots of a univariate nonlinear function

スポンサーリンク