A low-rank algorithm for solving Lyapunov operator φ-functions within the matrix-valued exponential integrators
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In this work we develop a low-rank algorithm for the computation of low-rank approximations to the large-scale Lyapunov operator φ-functions. Such computations constitute the important ingredient to the implementation of matrix-valued exponential integrators for large-scale stiff matrix differential equations where the (approximate) solutions are of low rank. We evaluate the approximate solutions of LDL^T-type based on a scaling and recursive procedure. The key parameters of the method are determined using a quasi-backward error bound combined with the computational cost. Numerical results demonstrate that our method can be used as a basis of matrix-valued exponential integrators for solving large-scale differential Lyapunov equations and differential Riccati equations.
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