Search

This paper aims at finding a fixed-time solution to the Sylvester equation by using a gradient neural network (GNN). To reach this goal, a modified sign-bi-power (msbp) function is presented and applied on a linear GNN as an activation function. Accordingly, a fixed-time convergent GNN (FTC-GNN) model is developed for solving the Sylvester equation. The upper bound of the convergence time of such an FTC-GNN model can be predetermined if parameters are given regardless of the initial conditions. This point is corroborated by a detailed theoretical analysis. In addition, the convergence time is also estimated utilizing the Lyapunov stability theory. Two examples are then simulated to demonstrate the validation of the theoretical analysis, as well as the superior convergence performance of the presented FTC-GNN model as compared to the existing GNN models. [ABSTRACT FROM AUTHOR]

In this paper, we seek connections between the Sylvester equation and Kadomtsev–Petviashvili system. By introducing Sylvester equation L M are bold, please chekc if bold neceaasry, if not, please remove all bold of equation − M K = r s T together with an evolution equation set of r and s , master function S (i , j) = s T K j C (I + M C) − 1 L i r is used to construct the Kadomtsev–Petviashvili system, including the Kadomtsev–Petviashvili equation, modified Kadomtsev–Petviashvili equation and Schwarzian Kadomtsev–Petviashvili equation. The matrix M provides τ -function by τ = | I + M C |. With the help of some recurrence relations, the reductions to the Korteweg–de Vries and Boussinesq systems are discussed. [ABSTRACT FROM AUTHOR]

In order to solve the Sylvester equations more efficiently, a new four parameters positive and skew-Hermitian splitting (FPPSS) iterative method is proposed in this paper based on the previous research of the positive and skew-Hermitian splitting (PSS) iterative method. We prove that when coefficient matrix A and B satisfy certain conditions, the FPPSS iterative method is convergent in the parameter's value region. The numerical experiment results show that compared with previous iterative method, the FPPSS iterative method is more effective in terms of iteration number IT and runtime. [ABSTRACT FROM AUTHOR]