Accurate quotient-difference algorithm: Error analysis, improvements and applications

作者：Du Peibing; Barrio Roberto; Jiang Hao^*; Cheng Lizhi

来源：Applied Mathematics and Computation, 2017, 309: 245-271.

DOI：10.1016/j.amc.2017.04.004

• Qd algorithm
• Compensated qd algorithm
• Error-free transformation
• Rounding error
• Continued fractions
• Pole detection

The compensated quotient-difference (Compqd) algorithm is proposed along with some applications. The main motivation is based on the fact that the standard quotient difference (qd) algorithm can be numerically unstable. The Compqd algorithm is obtained by applying error-free transformations to improve the traditional qd algorithm. We study in detail the error analysis of the qd and Compqd algorithms and we introduce new condition numbers so that the relative forward rounding error bounds can be derived directly. Our numerical experiments illustrate that the Compqd algorithm is much more accurate than the qd algorithm, relegating the influence of the condition numbers up to second order in the rounding unit of the computer. Three applications of the new algorithm in the obtention of continued fractions and in pole and zero detection are shown.

• 出版日期2017-9-15
• 单位中国人民解放军国防科学技术大学