General fixed-point method for solving the linear complementarity problem
Keyword(s):
<abstract><p>In this paper, we consider numerical methods for the linear complementarity problem (LCP). By introducing a positive diagonal parameter matrix, the LCP is transformed into an equivalent fixed-point equation and the equivalence is proved. Based on such equation, the general fixed-point (GFP) method with two cases are proposed and analyzed when the system matrix is a $ P $-matrix. In addition, we provide several concrete sufficient conditions for the proposed method when the system matrix is a symmetric positive definite matrix or an $ H_{+} $-matrix. Meanwhile, we discuss the optimal case for the proposed method. The numerical experiments show that the GFP method is effective and practical.</p></abstract>
2011 ◽
Vol 340
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pp. 3-8
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2011 ◽
Vol 152
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pp. 739-772
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2016 ◽
Vol 32
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pp. 921-932
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1990 ◽
Vol 132
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pp. 123-136
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2012 ◽
Vol 40
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pp. 484-486
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2008 ◽
pp. 283-293
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