# LAPACK-Style Algorithms and Software for Solving the Generalized Sylvester Equation and Estimating the Separation Between Regular Matrix Pairs

```@article{Kgstrm1996LAPACKStyleAA,
title={LAPACK-Style Algorithms and Software for Solving the Generalized Sylvester Equation and Estimating the Separation Between Regular Matrix Pairs},
author={Bo K{\aa}gstr{\"o}m and Peter Poromaa},
journal={ACM Trans. Math. Softw.},
year={1996},
volume={22},
pages={78-103}
}```
Robust and fast software to solve the generalized Sylvester equation (AR - LB = C, DR - LE = F) for unknowns R and L is presented. This special linear system of equations, and its transpose, arises in computing error bounds for computed eigenvalues and eigenspaces of the generalized eigenvalue problem S-λT, in computing deflating subspaces of the same problem, and in computing certain decompositions of transfer matrices arising in control theory. Our contributions are twofold. First, we… CONTINUE READING

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