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This paper aims to show that the existing preconditioned symmetric successive over-relaxation (SSOR) approach to solving the linear complementarity problem (LCP) is not valid. To overcome the flaws, we propose an efficient preconditioner called the monomial preconditioner. The convergence behavior of the proposed model is also established. Meanwhile, the efficiency of the new method is verified by numerical experiments.INDEX TERMS Linear complementarity problem, M-matrix, preconditioning, projected model, SSOR method.

We deal with the problem of uniqueness of a meromorphic function sharing one small function with its k's derivative and obtain some results.

This paper investigates the combined damped sinusoidal oscillation solutions to the 3 + 1 -D variable-coefficient (VC) generalized nonlinear wave equation. The bilinear form is considered in terms of Hirota derivatives. Accordingly, we utilize a binary Bell polynomial transformation for reducing the Cole-Hopf algorithm to get the exact solutions of the VC generalized NLW equation. The damped sinusoidal oscillations for two cases of the nonlinear wave ordinary differential equation will be studied. Using suitable mathematical assumptions, the novel kinds of solitary, periodic, and singular soliton solutions are derived and established in view of the trigonometric and rational functions of the governing equation. To achieve this, the illustrative example of the VC generalized nonlinear wave equation is provided to demonstrate the feasibility and reliability of the procedure used in this study. The trajectory solutions of the traveling waves are shown explicitly and graphically. The effect of the free parameters on the behavior of acquired figures of a few obtained solutions for two nonlinear rational exact cases was also discussed. By comparing the proposed method with the other existing methods, the results show that the execution of this method is concise, simple, and straightforward.