Parallel Krylov subspace methods for solving Sylvester's equations.

摘要

Some problems in applied mathematics can be formulated as a Sylvester's equation of the form {dollar}AX-XB=C{dollar}. For the solution of such equations, iterative methods are often preferred, especially when both A and B are large and sparse. We present parallel iterative methods for the solution of Sylvester's equations. The algorithms use tensor products of Krylov subspaces for which orthonormal bases are generated by the Arnoldi process. For certain choices of subspaces, the computation of the solution splits into the solution of many independent subproblems, and therefore can be carried out in parallel. We also present numerical experience of implementations of our algorithms on a shared-memory parallel computer and a network of workstations connected as a distributed-memory computer.