Row-wise algorithms of ST decomposition

New row-wise algorithms for the ST decomposition are established here. The new algorithms require just a row of A and two triangular solvers at each step instead of three triangular solvers in Golub–Yuan algorithms (BIT, 42 (2002) 814–822). Therefore, multiplication and storage requirements of the ST decomposition can greatly be saved in the row-wise algorithms. Some numerical comparisons are presented. It follows from numerical experiments that the new algorithms save at least 40% CPU time compared with other algorithms of the ST decomposition. In terms of numerical experiments, the numerical stability of the new algorithms is reasonable.