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On the numerical solution ofAX −XB =C

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Abstract

In this note we analyze the numerical solution ofAX −XB =C when a Galerkin method is applied, assuming thatB has much smaller size thanA. We show that the corresponding Galerkin equation can be obtained from the truncation of the original problem, if matrix polynomials are used for writing the analytical solutionX. Moreover, we provide some relations between the separation ofA andB in their natural space and that in the projected space. Experimental tests validate some of the theoretical results and show the rate of applicability of the method with respect to a standard linear system solver.

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Authors and Affiliations

  1. Istituto di Analisi Numerica, Consiglio Nazionale delle Ricerche, via Abbiategrasso 209, 1-27100, Pavia, Italy

    V. Simoncini

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  1. V. Simoncini
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Part of this work was done while the author was at the Dipartimento di Fisica, Universitá di Bologna, Italy.

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Simoncini, V. On the numerical solution ofAX −XB =C . Bit Numer Math 36, 814–830 (1996). https://doi.org/10.1007/BF01733793

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  • DOI: https://doi.org/10.1007/BF01733793

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