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

Syaida Fadhilah Mohammad Rusli, Mansor Monsi, Nasruddin Hassan, Norazak Senu, Fudziah Ismail, Zarina Bibi Ibrahim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

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 languageEnglish
Title of host publicationAIP Conference Proceedings
PublisherAmerican Institute of Physics Inc.
Volume1682
ISBN (Print)9780735413290
DOIs
Publication statusPublished - 22 Oct 2015
Event22nd National Symposium on Mathematical Sciences: Strengthening Research and Collaboration of Mathematical Sciences in Malaysia, SKSM 2014 - Selangor, Malaysia
Duration: 24 Nov 201426 Nov 2014

Other

Other22nd National Symposium on Mathematical Sciences: Strengthening Research and Collaboration of Mathematical Sciences in Malaysia, SKSM 2014
CountryMalaysia
CitySelangor
Period24/11/1426/11/14

Fingerprint

polynomials
intervals
iteration

Keywords

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

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Rusli, S. F. M., Monsi, M., Hassan, N., Senu, N., Ismail, F., & Ibrahim, Z. B. (2015). On modified interval repeated zoro symmetric single-step IRZSS1-5D procedure for bounding polynomial zeros simultaneously. In 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.

AIP Conference Proceedings. Vol. 1682 American Institute of Physics Inc., 2015. 020011.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Rusli, SFM, Monsi, M, Hassan, N, Senu, N, Ismail, F & Ibrahim, ZB 2015, On modified interval repeated zoro symmetric single-step IRZSS1-5D procedure for bounding polynomial zeros simultaneously. in 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
Rusli SFM, Monsi M, Hassan N, Senu N, Ismail F, Ibrahim ZB. On modified interval repeated zoro symmetric single-step IRZSS1-5D procedure for bounding polynomial zeros simultaneously. In AIP Conference Proceedings. Vol. 1682. American Institute of Physics Inc. 2015. 020011 https://doi.org/10.1063/1.4932420
Rusli, Syaida Fadhilah Mohammad ; Monsi, Mansor ; Hassan, Nasruddin ; Senu, Norazak ; Ismail, Fudziah ; Ibrahim, Zarina Bibi. / On modified interval repeated zoro symmetric single-step IRZSS1-5D procedure for bounding polynomial zeros simultaneously. AIP Conference Proceedings. Vol. 1682 American Institute of Physics Inc., 2015.
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AU - Senu, Norazak

AU - Ismail, Fudziah

AU - Ibrahim, Zarina Bibi

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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.

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