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Modified modulus-based matrix splitting iteration method for horizontal quasi-complementarity problems
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DOI：10.1016/j.cam.2025.117153.png)
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Abstract
En 中文
In this paper, by making use of the implicit fixed-point equation of the horizontal quasicomplementarity problem (HQCP) and the relations between the auxiliary vectors and solution vectors, we design a modified modulus-based matrix splitting (MMMS) iteration method for solving the HQCP. Compared with the MMS method (Commu. Appl. Math. Comput., 2023) proposed very recently, the MMMS iteration method does not involve inner iterations and its initial vector can be adopted unlimitedly. And it is no need to solve a linear subsystem with the coefficient matrix B in each iteration of the MMMS method. Hence the proposed MMMS method may own higher computational efficiency than the MMS one in practical application. Besides, we study the convergence conditions of the MMMS iteration method for two types of system matrices, which contain and generalize some related results. Also, the selection method for the parameter matrix of the MMMS method is proposed. At the end, the effectiveness and superiority of the MMMS method are verified by numerical experiments.
Keywords:
Horizontal quasi-complementarity problems
Implicit fixed-point equation
Modulus-based matrix splitting iteration method
Convergence
The selection of the parameter matrix
Journal
J
IF:
2.6
Papers:
336
Citations:
0