An iterative method to solve Lyapunov equations

09/21/2023

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by   Licio Hernanes Bezerra, et al.

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We present here a new splitting method to solve Lyapunov equations in a Kronecker product form. Although this resulting matrix is of order n^2, each iteration demands two operations with the matrix A: a multiplication of the form (A-σ I) B̃ and a inversion of the form (A-σ I)^-1B̃. We see that for some choice of a parameter the iteration matrix is such that all their eigenvalues are in absolute value less than 1. Moreover we present a theorem that enables us to get a good starting vector for the method.