• Abstract

An operator $T$ on a separable, infinite dimensional, complex Hilbert space $\mathcal{H}$ is called conjugate normal if $C|T|C = |T^∗|$ for some conjugate linear, isometric involution $C$ on $\mathcal{H}.$ This paper focuses on the invariance of conjugate normality under similarity. Given an operator $T,$ we prove that every operator $A$ similar to $T$ is conjugate normal if and only if there exist complex numbers $λ_1$,$λ_2$ such that $(T−λ_1)(T−λ_2)=0.$

• General Summary

• Abstract

Recently, Yu et al. presented a modified fixed point iterative (MFPI) method for solving large sparse absolute value equation (AVE). In this paper, we consider using accelerated overrelaxation (AOR) splitting to develop the modified fixed point iteration (denoted by MFPI-JS and MFPI-GSS) methods for solving AVE. Furthermore, the convergence analysis of the MFPI-JS and MFPI-GSS methods for AVE are also studied under suitable restrictions on the iteration parameters, and the functional equation between the parameter $\tau$ and matrix $Q.$ Finally, numerical examples show that the MFPI-JS and MFPI-GSS are efficient iteration methods.

• General Summary