Convergence-Accelerated Fixed-Time Dynamical Methods for Absolute Value Equations

Two new accelerated fixed-time stable dynamic systems are proposed for solving absolute value equations (AVEs): \(Ax-|x|-b=0\). Under some mild conditions, the equilibrium point of the proposed dynamic systems is completely equivalent to the solution of the AVEs under consideration. Meanwhile, we have introduced a new relatively tighter global error bound for the AVEs. Leveraging this finding, we have separately established the globally fixed-time stability of the proposed methods, along with providing the conservative settling-time for each method. Compared with some existing state-of-the-art dynamical methods, preliminary numerical experiments show the effectiveness of our methods in solving the AVEs.