Abstract
We describe Galerkin and minimal residual algorithms for the solution of Sylvester's equation AX – XB = C. The algorithms use Krylov subspaces forwhich orthogonal bases are generated by the Arnoldi process. For certain choices of Krylov subspaces the computation of the solution splits into the solution of many independent subproblems. This makes the algorithms suitable for implementation on parallel computers.
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