### Abstract

The point symmetric single-step procedure established by Monsi (2012) has R-order of convergence at least 3. This procedure is modified by repeating the steps in the procedure r times without involving function evaluations. This modified procedure is called the point repeated symmetric single-step PRSS1. The R-order of convergence of PRSS1 is at least (2r + 1) (r=1). Computational experiences in the implementation of the interval version of PRSS1 (see Monsi and Wolfe, 1988) showed that the repeated symmetric single-step procedure is more efficient than the total step (Kerner, 1966) and the single-step (Alefeld and Herzberger, 1974) methods.

Original language | English |
---|---|

Pages (from-to) | 301-315 |

Number of pages | 15 |

Journal | Malaysian Journal of Mathematical Sciences |

Volume | 9 |

Issue number | 2 |

Publication status | Published - 2015 |

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### Keywords

- Point procedure
- R-order of convergence
- Simple zeros
- Simultaneous estimation

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Malaysian Journal of Mathematical Sciences*,

*9*(2), 301-315.

**On the convergence of the point repeated symmetric single-step procedure for simultaneous estimation of polynomial zeros.** / Monsi, Mansor; Rusli, Syaida Fadhilah Muhamad; Hassan, Nasruddin; Ismail, Fudziah; Ibrahim, Zarina Bibi.

Research output: Contribution to journal › Article

*Malaysian Journal of Mathematical Sciences*, vol. 9, no. 2, pp. 301-315.

}

TY - JOUR

T1 - On the convergence of the point repeated symmetric single-step procedure for simultaneous estimation of polynomial zeros

AU - Monsi, Mansor

AU - Rusli, Syaida Fadhilah Muhamad

AU - Hassan, Nasruddin

AU - Ismail, Fudziah

AU - Ibrahim, Zarina Bibi

PY - 2015

Y1 - 2015

N2 - The point symmetric single-step procedure established by Monsi (2012) has R-order of convergence at least 3. This procedure is modified by repeating the steps in the procedure r times without involving function evaluations. This modified procedure is called the point repeated symmetric single-step PRSS1. The R-order of convergence of PRSS1 is at least (2r + 1) (r=1). Computational experiences in the implementation of the interval version of PRSS1 (see Monsi and Wolfe, 1988) showed that the repeated symmetric single-step procedure is more efficient than the total step (Kerner, 1966) and the single-step (Alefeld and Herzberger, 1974) methods.

AB - The point symmetric single-step procedure established by Monsi (2012) has R-order of convergence at least 3. This procedure is modified by repeating the steps in the procedure r times without involving function evaluations. This modified procedure is called the point repeated symmetric single-step PRSS1. The R-order of convergence of PRSS1 is at least (2r + 1) (r=1). Computational experiences in the implementation of the interval version of PRSS1 (see Monsi and Wolfe, 1988) showed that the repeated symmetric single-step procedure is more efficient than the total step (Kerner, 1966) and the single-step (Alefeld and Herzberger, 1974) methods.

KW - Point procedure

KW - R-order of convergence

KW - Simple zeros

KW - Simultaneous estimation

UR - http://www.scopus.com/inward/record.url?scp=84929927431&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929927431&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84929927431

VL - 9

SP - 301

EP - 315

JO - Malaysian Journal of Mathematical Sciences

JF - Malaysian Journal of Mathematical Sciences

SN - 1823-8343

IS - 2

ER -