We derive a conjugate-gradient type algorithm to produce approximate least-squares (LS) solutions for an inconsistent generalized Sylvester-transpose matrix equation. The is always applicable any given initial and will arrive at LS solution within finite steps. When the equation has many solutions, can search one with minimal Frobenius-norm. Moreover, Y, find unique closest Y. Numerical experim...

This paper addresses two problems: an image denoising problem assuming dense observations and an image reconstruction problem from sparse data. It shows that both problems can be solved by the Sylvester/Lyapunov algebraic equation. The Sylvester/Lyapunov equation has been extensively studied in Control Theory and it can be efficiently solved by well known numeric algorithms. This paper proposes...

The Sylvester smallest enclosing circle problem involves finding the smallest circle that encloses a finite number of points in the plane. We consider generalized versions of the Sylvester problem in which the points are replaced by sets. Based on the log-exponential smoothing technique and Nesterov’s accelerated gradient method, we present an effective numerical algorithm for solving these pro...

The global FOM and GMRES algorithms are among the effective methods to solve Sylvester matrix equations. In this paper, we study these algorithms in the case that the coefficient matrices are real symmetric (real symmetric positive definite) and extract two CG-type algorithms for solving generalized Sylvester matrix equations. The proposed methods are iterative projection methods onto matrix Kr...

Abstract In this paper, we consider skew-Hermitian solution of coupled generalized Sylvester matrix equations encompassing $$*$$ ∗ -hermicity over complex field. The compact formula the general system is presented in terms inverses when some necessary and sufficient conditi...

This paper is devoted to proposing a modified conjugate residual method for solving the generalized coupled Sylvester tensor equations. To further improve its convergence rate, we derive preconditioned based on Kronecker product approximations A theoretical analysis shows that proposed converges an exact solution any initial at most finite steps in absence round-off errors. Compared with gradie...

In this paper, we consider large-scale linear discrete ill-posed problems where the right-hand side contains noise. Regularization techniques such as Tikhonov regularization are needed to control the effect of the noise on the solution. In many applications such as in image restoration the coefficient matrix is given as a Kronecker product of two matrices and then Tikhonov regularization proble...

By using a generalized Sylvester equation based parametrization, three minimum norm robust pole assignment problems for descriptor systems are formulated as unconstrained minimization problems for suitably chosen cost functions. The derived explicit expressions of the gradients of the cost functions allow the efficient solution of the minimization problems by using powerful gradient search base...