Abstract We consider here the LU factorisation of the solution to a Stein and discrete Lyapunov equation. We show how the K × K matrix solution P to a general Stein equation can, under mild conditions, be factorised in a product without actually computing P . If the coeffi- cients of P are lower and upper triangular, the factorisation thus ob- tained is and LU factorisation in K3 flops. Moreover, we show that, if special matrices like Bezoutians, and Loewner, Pick, and Toeplitz ma- trices, admit an LU factorisation, this can be computed in K2 flops. Similarly the computation of their inverses requires the same com- plexity.
LU factorisation of special matrices satisfying the Stein equation.
2020
Abstract
Abstract We consider here the LU factorisation of the solution to a Stein and discrete Lyapunov equation. We show how the K × K matrix solution P to a general Stein equation can, under mild conditions, be factorised in a product without actually computing P . If the coeffi- cients of P are lower and upper triangular, the factorisation thus ob- tained is and LU factorisation in K3 flops. Moreover, we show that, if special matrices like Bezoutians, and Loewner, Pick, and Toeplitz ma- trices, admit an LU factorisation, this can be computed in K2 flops. Similarly the computation of their inverses requires the same com- plexity.File in questo prodotto:
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