An alternating direction method for nonnegative solutions of the matrix equation $$AX+YB=C$$ A X + Y B = C

Abstract

In this paper, an alternating direction method (ADM) is proposed for nonnegative solutions of the matrix equation AX + Y B = C. In addition, the preliminary convergence of the proposed method is given and proved. Numerical experiments illustrate the effectiveness of the method.

Iterative Algorithms for Symmetric Positive Semidefinite Solutions of the Lyapunov Matrix Equations

“…In this section, motivated by the alternating direction methods of multiplier (ADMM) in [12,13], we shall present the third iterative algorithm for the constrained Lyapunov matrix equations and discuss its convergence. Firstly, CMO (8) can be written as the following equivalent form:…”

“…An appealing characteristic of the method proposed by Huang and Ma [11] is that: (i) it has finite termination property in the absence of round-off errors; (ii) it can obtain least Frobenius norm solution of problem (1) when it adopts some special kind of initial matrix. Furthermore, Ke and Ma [12] extended the alternating direction method of multipliers (ADMM), which is a famous numerical method in separable optimization programming, to solve problem (1) with the nonnegative constraint X * ≥ 0, which is obviously motivated by the design principle proposed by Xu et al [13].…”

Extremal values of vertex‐degree‐based topological indices of coronoid systems

“…In the mathematical chemistry literature, there are several studies about graph theoretical applications to coronoid systems. [ 30–40 ] In the case of topological indices, the expression for a number of distance‐based topological indices of circumcised donut benzenoid systems were obtained in Arockiaraj et al [ 34 ] In Kulli et al, [ 41 ] the values of new topological indices derived from the augmented Zagreb index were computed for the zigzag‐edge coronoid fused with starphene nanotube ZCS (k, l, m). The expressions for computing the values of nine VDB topological indices for r ‐circumscribed coronoid systems were obtained in Julietraja and Venugopal.…”