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<p>In this article, we establish a class of new projected iterative methods based on matrix splitting for solving the linear complementarity problem. We provide a fixed-point equation and demonstrate that this equation is equivalent to a linear complementarity problem. Also, we provide some convergence conditions for the proposed method when the system matrix is either a <i>P</i>-matrix or an <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12044_2025_844_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>-matrix. Several numerical examples demonstrate the effectiveness of the suggested methods, which are superior to the modulus-based matrix splitting methods in terms of the number of iteration steps and the time required by the CPU.</p>

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More on projected type iteration method and linear complementarity problem

  • 期刊论文

  • 发表日期：

    2025年11月8日

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  • A K Das,
  • Deepmala,
  • Bharat Kumar

摘要

In this article, we establish a class of new projected iterative methods based on matrix splitting for solving the linear complementarity problem. We provide a fixed-point equation and demonstrate that this equation is equivalent to a linear complementarity problem. Also, we provide some convergence conditions for the proposed method when the system matrix is either a P-matrix or an \(H_+\) H + -matrix. Several numerical examples demonstrate the effectiveness of the suggested methods, which are superior to the modulus-based matrix splitting methods in terms of the number of iteration steps and the time required by the CPU.