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<p>In this work, for solving horizontal linear complementarity problems, an inner–outer iteration method is established, which can be seen as a two-stage iteration method where the inner iteration contains the modulus-based matrix splitting iteration. The convergence conditions are given for the proposed method based on <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3373_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_+\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mo>+</mo> </msub> </math></EquationSource> </InlineEquation>-matrices assumptions. Specially, the theoretical results with respect to the popularly accelerated overrelaxation method is presented. Finally, numerical examples are illustrated to show the efficiency of proposed method.</p>

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An inner–outer modulus-based method for solving horizontal linear complementarity problems

  • 期刊论文

  • 发表日期：

    2025年8月19日

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  • Yongxiong Zhang,
  • Hua Zheng,
  • Seakweng Vong

摘要

In this work, for solving horizontal linear complementarity problems, an inner–outer iteration method is established, which can be seen as a two-stage iteration method where the inner iteration contains the modulus-based matrix splitting iteration. The convergence conditions are given for the proposed method based on \(H_+\) H + -matrices assumptions. Specially, the theoretical results with respect to the popularly accelerated overrelaxation method is presented. Finally, numerical examples are illustrated to show the efficiency of proposed method.