Block algorithms for reordering standard and generalized Schur forms
ACM Transactions on Mathematical Software (TOMS)
Solving linear-quadratic optimal control problems on parallel computers
Optimization Methods & Software
An invariant subspace method for large-scale algebraic Riccati equation
Applied Numerical Mathematics
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The matrix sign function has several applications in system theory and matrix computations. However, the numerical behavior of the matrix sign function, and its associated divide-and-conquer algorithm for computing invariant subspaces, are still not completely understood. In this paper, we present a new perturbation theory for the matrix sign function, the conditioning of its computation, the numerical stability of the divide-and-conquer algorithm, and iterative refinement schemes. Numerical examples are also presented. An extension of the matrix-sign-function-based algorithm to compute left and right deflating subspaces for a regular pair of matrices is also described.