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Two-step modulus-based matrix splitting iteration method for horizontal implicit complementarity problems
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DOI：10.1007/s40314-025-03544-w.png)
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Abstract
En 中文
The well-known modulus-based matrix splitting (MMS) iteration method has been successfully extended to solve the horizontal implicit complementarity problem. However, due to the existence of two system matrices and one nonlinear term, in order to satisfy the nonnegative and orthogonal constraints, a linear system and a weakly nonlinear system must be solved at each step of the MMS iteration method. This costs very expensive. To effectively accelerate the convergence rate of the MMS iteration method so as to enhance its computational efficiency, based on the idea of the two-step matrix splitting paradigm, a two-step MMS (TMMS) iteration method is proposed. Implementation aspects are discussed in detail. Theoretical analyses about the convergence conditions of the TMMS iteration method are carefully studied when the system matrices are positive definite matrices and H $$_+$$ -matrices, respectively. Finally, two numerical examples are used to illustrate the performance of the proposed TMMS iteration method.
Keywords:
Horizontal implicit complementarity problem
Modulus-based iteration method
Matrix splitting
Two-step iteration method
Convergence
Journal
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Papers:
266
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