Cholesky-like factorizations of skew-symmetric matrices
The authors present a stable \(O(n^3)\) algorithm for computing \(R\) in the Cholesky-like factorization \(B= R^TJR\) of some skew-symmetric \(2n\times 2n\) matrix \(B\), where \(R\) is a permuted triangular matrix and \(J\) has the form \[ J= \left[\begin{matrix} O & I_n\\ -I_n & 0\end{matrix}\right]. \] Cholesky-like factorizations of skew-symmetric matrices are needed in the treatment of generalized eigenvalue problems with Hamiltonian structure that arise, e.g., in the analysis of corner singularities in elasticity and in linear quadratic optimal control problems. These applications are also discussed in the paper.
linear quadratic optimal control problems
scientific article; zbMATH DE number 1533611
scientific article