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

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 impro...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 309; pp. 245 - 271
Main Authors: Du, Peibing, Barrio, Roberto, Jiang, Hao, Cheng, Lizhi
Format: Journal Article
Language:English
Published: Elsevier Inc 15.09.2017
Subjects:
Compensated qd algorithm
Continued fractions
Error-free transformation
Pole detection
Qd algorithm
Rounding error
Rounding error
Compensated qd algorithm
Qd algorithm
Pole detection
Error-free transformation
Continued fractions
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2017.04.004