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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| Veröffentlicht in: | Applied mathematics and computation Jg. 309; S. 245 - 271 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Du, Peibing Jiang, Hao Barrio, Roberto Cheng, Lizhi |
| Author_xml | – sequence: 1 givenname: Peibing orcidid: 0000-0002-7971-7842 surname: Du fullname: Du, Peibing email: dupeibing10@nudt.edu.cn organization: School of Science, National University of Defense Technology, Changsha 410073, China – sequence: 2 givenname: Roberto surname: Barrio fullname: Barrio, Roberto email: rbarrio@unizar.es organization: Departamento de Matemática Aplicada and IUMA, University of Zaragoza, Zaragoza E-50009, Spain – sequence: 3 givenname: Hao surname: Jiang fullname: Jiang, Hao email: haojiang@nudt.edu.cn, jhnudt@163.com organization: College of Computer, National University of Defense Technology, Changsha 410073, China – sequence: 4 givenname: Lizhi surname: Cheng fullname: Cheng, Lizhi email: clzcheng@nudt.edu.cn organization: School of Science, National University of Defense Technology, Changsha 410073, China |
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| Cites_doi | 10.1017/S0370164600022070 10.1007/BF01601216 10.1145/365559.365619 10.1006/jsco.1997.0162 10.1017/S0370164600023026 10.1137/030601818 10.1016/j.camwa.2010.05.021 10.1093/imanum/drq003 10.1007/s002110050024 10.1137/07068816X 10.1007/BF03186531 10.1016/j.apnum.2010.03.016 10.1145/641876.641878 10.6028/jres.045.026 10.1016/j.apnum.2010.04.006 10.1137/050645671 10.1017/S096249291000005X 10.1007/BF01600331 10.1007/BF01397083 10.1145/567806.567808 |
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| Keywords | Rounding error Compensated qd algorithm Qd algorithm Pole detection Error-free transformation Continued fractions |
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| Snippet | The compensated quotient-difference (Compqd) algorithm is proposed along with some applications. The main motivation is based on the fact that the standard... |
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| SubjectTerms | Compensated qd algorithm Continued fractions Error-free transformation Pole detection Qd algorithm Rounding error |
| Title | Accurate quotient-difference algorithm: Error analysis, improvements and applications |
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