To the question of efficiency of iterative methods

Tamara Kogan; Luba Sapir; Amir Sapir; Ariel Sapir

doi:10.1016/j.aml.2016.11.006

To the question of efficiency of iterative methods

Tamara Kogan
, Luba Sapir
, Amir Sapir
, Ariel Sapir

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

In this paper we prove that, among all one-point iterative processes without memory of order p, the most efficient processes are of order p=3. Moreover, the computational efficiency of one-point iterative processes without memory decreases to 1 as p increases, i.e., the efficiency index of higher order of convergence methods is low. We find the upper and lower bounds of the Ostrowski–Traub index of computational efficiency in a wider class of iterative methods with unit informational efficiency.

Original language	English
Pages (from-to)	40-46
Number of pages	7
Journal	Applied Mathematics Letters
Volume	66
DOIs	https://doi.org/10.1016/j.aml.2016.11.006
State	Published - 1 Apr 2017

Keywords

Computational efficiency
Efficiency index
Informational efficiency
Iterative methods
One-point method without memory
Order of convergence

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aml.2016.11.006

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abstract = "In this paper we prove that, among all one-point iterative processes without memory of order p, the most efficient processes are of order p=3. Moreover, the computational efficiency of one-point iterative processes without memory decreases to 1 as p increases, i.e., the efficiency index of higher order of convergence methods is low. We find the upper and lower bounds of the Ostrowski–Traub index of computational efficiency in a wider class of iterative methods with unit informational efficiency.",

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AU - Kogan, Tamara

AU - Sapir, Luba

AU - Sapir, Amir

AU - Sapir, Ariel

PY - 2017/4/1

Y1 - 2017/4/1

N2 - In this paper we prove that, among all one-point iterative processes without memory of order p, the most efficient processes are of order p=3. Moreover, the computational efficiency of one-point iterative processes without memory decreases to 1 as p increases, i.e., the efficiency index of higher order of convergence methods is low. We find the upper and lower bounds of the Ostrowski–Traub index of computational efficiency in a wider class of iterative methods with unit informational efficiency.

AB - In this paper we prove that, among all one-point iterative processes without memory of order p, the most efficient processes are of order p=3. Moreover, the computational efficiency of one-point iterative processes without memory decreases to 1 as p increases, i.e., the efficiency index of higher order of convergence methods is low. We find the upper and lower bounds of the Ostrowski–Traub index of computational efficiency in a wider class of iterative methods with unit informational efficiency.

KW - Computational efficiency

KW - Efficiency index

KW - Informational efficiency

KW - Iterative methods

KW - One-point method without memory

KW - Order of convergence

UR - https://www.scopus.com/pages/publications/84999791885

U2 - 10.1016/j.aml.2016.11.006

DO - 10.1016/j.aml.2016.11.006

M3 - Article

AN - SCOPUS:84999791885

SN - 0893-9659

VL - 66

SP - 40

EP - 46

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

To the question of efficiency of iterative methods

Abstract

Keywords

ASJC Scopus subject areas

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