Two optimal Hager-Zhang conjugate gradient methods for solving monotone nonlinear equations

Jamilu Sabi'u; Abdullah Shah; Mohammed Yusuf Waziri

doi:10.1016/j.apnum.2020.02.017

Two optimal Hager-Zhang conjugate gradient methods for solving monotone nonlinear equations

Jamilu Sabi'u^*, Abdullah Shah, Mohammed Yusuf Waziri

^*Corresponding author for this work

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

51 Scopus citations

Abstract

We derived two adaptive choices for the nonnegative parameter of the Hager-Zhang conjugate gradient method. The first was achieved by minimizing the Frobenius condition number of the search direction matrix and the other by minimizing the difference between the smallest and the largest singular value. Global convergence is based on an appropriate assumption. Preliminary numerical results demonstrate the efficiency of the two adaptive choices.

Original language	English
Pages (from-to)	217-233
Number of pages	17
Journal	Applied Numerical Mathematics
Volume	153
DOIs	https://doi.org/10.1016/j.apnum.2020.02.017
State	Published - Jul 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2020 IMACS

Keywords

Condition number
Monotone nonlinear equations
Projection method
Singular value

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.apnum.2020.02.017

Cite this

@article{f5b6692213e04e12808ecddf2ae683aa,

title = "Two optimal Hager-Zhang conjugate gradient methods for solving monotone nonlinear equations",

abstract = "We derived two adaptive choices for the nonnegative parameter of the Hager-Zhang conjugate gradient method. The first was achieved by minimizing the Frobenius condition number of the search direction matrix and the other by minimizing the difference between the smallest and the largest singular value. Global convergence is based on an appropriate assumption. Preliminary numerical results demonstrate the efficiency of the two adaptive choices.",

keywords = "Condition number, Monotone nonlinear equations, Projection method, Singular value",

author = "Jamilu Sabi'u and Abdullah Shah and Waziri, {Mohammed Yusuf}",

note = "Publisher Copyright: {\textcopyright} 2020 IMACS",

year = "2020",

month = jul,

doi = "10.1016/j.apnum.2020.02.017",

language = "English",

volume = "153",

pages = "217--233",

journal = "Applied Numerical Mathematics",

issn = "0168-9274",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Two optimal Hager-Zhang conjugate gradient methods for solving monotone nonlinear equations

AU - Sabi'u, Jamilu

AU - Shah, Abdullah

AU - Waziri, Mohammed Yusuf

PY - 2020/7

Y1 - 2020/7

N2 - We derived two adaptive choices for the nonnegative parameter of the Hager-Zhang conjugate gradient method. The first was achieved by minimizing the Frobenius condition number of the search direction matrix and the other by minimizing the difference between the smallest and the largest singular value. Global convergence is based on an appropriate assumption. Preliminary numerical results demonstrate the efficiency of the two adaptive choices.

AB - We derived two adaptive choices for the nonnegative parameter of the Hager-Zhang conjugate gradient method. The first was achieved by minimizing the Frobenius condition number of the search direction matrix and the other by minimizing the difference between the smallest and the largest singular value. Global convergence is based on an appropriate assumption. Preliminary numerical results demonstrate the efficiency of the two adaptive choices.

KW - Condition number

KW - Monotone nonlinear equations

KW - Projection method

KW - Singular value

UR - http://www.scopus.com/inward/record.url?scp=85080086912&partnerID=8YFLogxK

U2 - 10.1016/j.apnum.2020.02.017

DO - 10.1016/j.apnum.2020.02.017

M3 - Article

AN - SCOPUS:85080086912

SN - 0168-9274

VL - 153

SP - 217

EP - 233

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

Two optimal Hager-Zhang conjugate gradient methods for solving monotone nonlinear equations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this