The Extended Abstract of The 5 th Seminar of Numerical Analysis and its Applications, 9-10 th Sep. 2014, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran CGLS METHOD FOR GENERAL COUPLED LINEAR MATRIX EQUATIONS OVER QUATERNIONS FATEMEH PANJEH ALI BEIK † , SALMAN AHMADI-ASL †, * AND DAVOD KHOJASTEH SALKUYEH ‡ † Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran f.beik@vru.ac.ir; p92357001@post.vru.ac.ir ‡ Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran khojasteh@guialn.ac.ir, salkuyeh@gmail.com Abstract. This paper deals with applying an iterative algorithm to find the least squares solution of the general coupled linear op- erator equations over quaternions number system. To this end, we develop the well-known conjugate gradient least squares (CGLS) algorithm. It can be theoretically shown that the offered algorithm converges to a solution of the mentioned problem in finite number of iterations in the exact arithmetic. 1. Introduction The quaternions are a part of modern mathematics and play a cardi- nal role in various areas such as computer graphics, control theory, sig- nal processing, and etc. We refer to [5] and the references therein which 2010 Mathematics Subject Classification. Primary 15A24; Secondary 15B33, 65F10. Key words and phrases. Quaternions, Matrix equation, CGLS algorithm. * Speaker. 1