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Title

A FINITE ITERATIVE ALGORITHM FOR SOLVING THE GENERALIZED REFLEXIVE SOLUTION OF THE COUPLED SYLVESTER-TRANSPOSE MATRIX EQUATIONS

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Abstract

 IN THIS WORK, BY EXTENDING THE IDEA OF CONJUGATE GRADIENT (CG) METHOD, WE PROPOSE AN ITERATIVE ALGORITHM TO COMPUTE A GENERALIZED REFLEXIVE SOLUTION PAIR OF THE COUPLED SYLVESTER-TRANSPOSE MATRIX EQUATIONS. WHEN THE PROBLEM IS CONSISTENT OVER THE GENERALIZED REFLEXIVE MATRIX PAIR [X, Y], FOR ANY GENERALIZED REFLEXIVE INITIAL ITERATIVE MATRIX PAIR [X 1; Y 1], THE UNIQUE LEAST-NORM GENERALIZED REFLEXIVE SOLUTION CAN BE OBTAINED WITHIN FINITE ITERATIVE STEPS IN THE ABSENCE OF ROUNDOFF ERRORS. FINALLY, SOME NUMERICAL EXAMPLES ARE PRESENTED TO SUPPORT THE THEORETICAL RESULTS OF THIS PAPER.

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