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Volume 15, Issue 1
A Relaxation Two-Step Newton-Based Matrix Splitting Iteration Method for Generalized Absolute Value Equations Associated with Circular Cones

Dongmei Yu, Yinghui Gao, Cairong Chen & Deren Han

DOI: 10.4208/eajam.2023-172.281023

East Asian J. Appl. Math., 15 (2025), pp. 138-162.

Published online: 2025-01

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  • Abstract

A relaxation two-step Newton-based matrix splitting (RTNMS) iteration method is proposed to solve the generalized absolute value equations associated with circular cones (CCGAVE). The convergence of the RTNMS iteration method is investigated under suitable conditions. Numerical results illustrate that the RTNMS iteration method is feasible and effective for solving the CCGAVE. Moreover, some sufficient conditions for the unique solvability of the CCGAVE are given.

  • Keywords

Generalized absolute value equations, circular cone, Newton-based matrix splitting method, convergence analysis.

  • AMS Subject Headings

65F10, 65H10, 90C30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-15-138, author = {Yu , DongmeiGao , YinghuiChen , Cairong and Han , Deren}, title = {A Relaxation Two-Step Newton-Based Matrix Splitting Iteration Method for Generalized Absolute Value Equations Associated with Circular Cones}, journal = {East Asian Journal on Applied Mathematics}, year = {2025}, volume = {15}, number = {1}, pages = {138--162}, abstract = {

A relaxation two-step Newton-based matrix splitting (RTNMS) iteration method is proposed to solve the generalized absolute value equations associated with circular cones (CCGAVE). The convergence of the RTNMS iteration method is investigated under suitable conditions. Numerical results illustrate that the RTNMS iteration method is feasible and effective for solving the CCGAVE. Moreover, some sufficient conditions for the unique solvability of the CCGAVE are given.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2023-172.281023}, url = {http://global-sci.org/intro/article_detail/eajam/23744.html} }
TY - JOUR T1 - A Relaxation Two-Step Newton-Based Matrix Splitting Iteration Method for Generalized Absolute Value Equations Associated with Circular Cones AU - Yu , Dongmei AU - Gao , Yinghui AU - Chen , Cairong AU - Han , Deren JO - East Asian Journal on Applied Mathematics VL - 1 SP - 138 EP - 162 PY - 2025 DA - 2025/01 SN - 15 DO - http://doi.org/10.4208/eajam.2023-172.281023 UR - https://global-sci.org/intro/article_detail/eajam/23744.html KW - Generalized absolute value equations, circular cone, Newton-based matrix splitting method, convergence analysis. AB -

A relaxation two-step Newton-based matrix splitting (RTNMS) iteration method is proposed to solve the generalized absolute value equations associated with circular cones (CCGAVE). The convergence of the RTNMS iteration method is investigated under suitable conditions. Numerical results illustrate that the RTNMS iteration method is feasible and effective for solving the CCGAVE. Moreover, some sufficient conditions for the unique solvability of the CCGAVE are given.

Yu , DongmeiGao , YinghuiChen , Cairong and Han , Deren. (2025). A Relaxation Two-Step Newton-Based Matrix Splitting Iteration Method for Generalized Absolute Value Equations Associated with Circular Cones. East Asian Journal on Applied Mathematics. 15 (1). 138-162. doi:10.4208/eajam.2023-172.281023
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