### Abstract

We present a new rapidly convergence procedure called the interval repeated zoro symmetric single-step IRZSS1-5D which is an extension of the procedures IZSS1-5D and IRSS1. Theoretical analysis shows that the rate of convergence of IRZSS1-5D is at least 3r + 2 (r ≥ 1), whereas the rates of convergence of IZSS1-5D and IRSS1 are at least five and 2r + 1 (r ≥ 1), respectively. With r = 1, the procedure IRZSS1-5D is identical to IZSS1-5D. The procedures IRSS1 and IZSS1-5D are the basic references for the establishment of IRZSS1-5D, where the forward-backward-forward (FBF) step of IZSS1-5D are repeated r times in IRZSS1-5D, so that some elements of FBF of IZSS1-5D can be saved and reused for the next inner iterations r = 2,3, ... in IRZSS1-5D.

Original language | English |
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Title of host publication | AIP Conference Proceedings |

Publisher | American Institute of Physics Inc. |

Volume | 1682 |

ISBN (Print) | 9780735413290 |

DOIs | |

Publication status | Published - 22 Oct 2015 |

Event | 22nd National Symposium on Mathematical Sciences: Strengthening Research and Collaboration of Mathematical Sciences in Malaysia, SKSM 2014 - Selangor, Malaysia Duration: 24 Nov 2014 → 26 Nov 2014 |

### Other

Other | 22nd National Symposium on Mathematical Sciences: Strengthening Research and Collaboration of Mathematical Sciences in Malaysia, SKSM 2014 |
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Country | Malaysia |

City | Selangor |

Period | 24/11/14 → 26/11/14 |

### Fingerprint

### Keywords

- Point procedure
- R-order of convergence
- simple zeros
- simultaneous inclusion

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*AIP Conference Proceedings*(Vol. 1682). [020011] American Institute of Physics Inc.. https://doi.org/10.1063/1.4932420

**On modified interval repeated zoro symmetric single-step IRZSS1-5D procedure for bounding polynomial zeros simultaneously.** / Rusli, Syaida Fadhilah Mohammad; Monsi, Mansor; Hassan, Nasruddin; Senu, Norazak; Ismail, Fudziah; Ibrahim, Zarina Bibi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*AIP Conference Proceedings.*vol. 1682, 020011, American Institute of Physics Inc., 22nd National Symposium on Mathematical Sciences: Strengthening Research and Collaboration of Mathematical Sciences in Malaysia, SKSM 2014, Selangor, Malaysia, 24/11/14. https://doi.org/10.1063/1.4932420

}

TY - GEN

T1 - On modified interval repeated zoro symmetric single-step IRZSS1-5D procedure for bounding polynomial zeros simultaneously

AU - Rusli, Syaida Fadhilah Mohammad

AU - Monsi, Mansor

AU - Hassan, Nasruddin

AU - Senu, Norazak

AU - Ismail, Fudziah

AU - Ibrahim, Zarina Bibi

PY - 2015/10/22

Y1 - 2015/10/22

N2 - We present a new rapidly convergence procedure called the interval repeated zoro symmetric single-step IRZSS1-5D which is an extension of the procedures IZSS1-5D and IRSS1. Theoretical analysis shows that the rate of convergence of IRZSS1-5D is at least 3r + 2 (r ≥ 1), whereas the rates of convergence of IZSS1-5D and IRSS1 are at least five and 2r + 1 (r ≥ 1), respectively. With r = 1, the procedure IRZSS1-5D is identical to IZSS1-5D. The procedures IRSS1 and IZSS1-5D are the basic references for the establishment of IRZSS1-5D, where the forward-backward-forward (FBF) step of IZSS1-5D are repeated r times in IRZSS1-5D, so that some elements of FBF of IZSS1-5D can be saved and reused for the next inner iterations r = 2,3, ... in IRZSS1-5D.

AB - We present a new rapidly convergence procedure called the interval repeated zoro symmetric single-step IRZSS1-5D which is an extension of the procedures IZSS1-5D and IRSS1. Theoretical analysis shows that the rate of convergence of IRZSS1-5D is at least 3r + 2 (r ≥ 1), whereas the rates of convergence of IZSS1-5D and IRSS1 are at least five and 2r + 1 (r ≥ 1), respectively. With r = 1, the procedure IRZSS1-5D is identical to IZSS1-5D. The procedures IRSS1 and IZSS1-5D are the basic references for the establishment of IRZSS1-5D, where the forward-backward-forward (FBF) step of IZSS1-5D are repeated r times in IRZSS1-5D, so that some elements of FBF of IZSS1-5D can be saved and reused for the next inner iterations r = 2,3, ... in IRZSS1-5D.

KW - Point procedure

KW - R-order of convergence

KW - simple zeros

KW - simultaneous inclusion

UR - http://www.scopus.com/inward/record.url?scp=84965148333&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84965148333&partnerID=8YFLogxK

U2 - 10.1063/1.4932420

DO - 10.1063/1.4932420

M3 - Conference contribution

AN - SCOPUS:84965148333

SN - 9780735413290

VL - 1682

BT - AIP Conference Proceedings

PB - American Institute of Physics Inc.

ER -