Iterative solution of the Lyapunov matrix equation
Applied Mathematics Letters
Application of ADI Iterative Methods to the Restoration of Noisy Images
SIAM Journal on Matrix Analysis and Applications
A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
SIAM Journal on Scientific Computing
ACM Transactions on Mathematical Software (TOMS)
Solution of the matrix equation AX + XB = C [F4]
Communications of the ACM
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
SIAM Journal on Matrix Analysis and Applications
A Preconditioner for Generalized Saddle Point Problems
SIAM Journal on Matrix Analysis and Applications
Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems
SIAM Journal on Scientific Computing
Low rank approximate solutions to large Sylvester matrix equations
Applied Mathematics and Computation
A new projection method for solving large Sylvester equations
Applied Numerical Mathematics
A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
SIAM Journal on Scientific Computing
On the ADI method for Sylvester equations
Journal of Computational and Applied Mathematics
Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation
SIAM Journal on Numerical Analysis
On Hermitian and skew-Hermitian splitting iteration methods for the linear matrix equation AXB=C
Computers & Mathematics with Applications
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In this paper, we present a positive-definite and skew-Hermitian splitting (PSS) iteration method for continuous Sylvester equations AX+XB=C with positive definite/semi-definite matrices. The theoretical analysis shows that the PSS iteration method will converge unconditionally and the optimal parameter of the new method is presented. Moreover, to reduce the computing cost, an inexact variant of the PSS iteration method (IPSS) and the analysis of its convergence property in detail have been established. Numerical results show that this new method and its inexact invariant are efficient and robust solvers for this class of continuous Sylvester equations.