A generalized eigenvalue approach for solving Riccati equations
(1981) SIAM Journal on Scientific and Statistical Computing — Vol. 2, n° 2, p. 121-135 (1981)
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- Abstract
- A numerically stable algorithm is derived to compute orthonormal bases for any deflating subspace of a regular pencil $lambda$B-A. The method is based on an update of the QZ -algorithm, in order to obtain any desired ordering of eigenvalues in the quasi-triangular forms constructed by this algorithm. As applications we discuss a new approach to solve Riccati equations arising in linear system theory. The computation of deflating subspaces with specified spectrum in shown to be of crucial importance here.
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Van Dooren, P. (1981). A generalized eigenvalue approach for solving Riccati equations. SIAM Journal on Scientific and Statistical Computing, 2(2), 121-135. https://hdl.handle.net/2078.5/71657 (Original work published 1981)