Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method
A new formulation of the low-rank Cholesky factor version of the alternating directions (ADI) implicit method is given. The proposed method generates real low-rank factors. It makes use of the dependence of iterates to complex conjugate shift parameters. This formulation reduces by half the amount of storage requirements and number of arithmetic calculations. Numerical results are given to show that the proposed algorithm is superior to the other presently known methods. The proposed method is tested on generalized Lyapunov and algebraic Riccati equations with large and sparse matrices and is also found superior in these instances.
alternating directions (ADI) implicit method
scientific article; zbMATH DE number 6136617
scientific article