A PARALLEL TRIANGULAR SYLVESTER EQUATION SOLVER BASED ON THE HESSENBERG-SCHUR METHOD∗
Enrique S. Quintana, Mercedes Marqués, Vicente Hernández · International Journal of Parallel Emergent and Distributed Systems · 1995
The Hessenberg-Schur method is one of the most efficient and stable algorithms for solving linear matrix equations. When it is applied to the Sylvester equation, AX + X B = C, matrix A is reduced to the Hessenberg form and matrix B to the real Schur for using orthogonal similarity transformations. In this paper we present a parallel algorithm for solving the Sylvester matrix equation when A and B are in the above-mentioned forms on a Distributed Memory Multiprocessor. Both a complexity analysis and an experimental study of the new algorithm are also presented.