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A Refined Block Arnoldi Method for Solving Large-Scale Lyapunov Equations
Un método de Arnoldi de bloques refinados para resolver ecuaciones de Lyapunov de gran escala
DOI:
https://doi.org/10.15446/recolma.v60n1.129103Palabras clave:
Krylov subspaces, Block Arnoldi process, Lyapunov equation (en)Subespacios de Krylov, proceso de Arnoldi por bloques, ecuación de Lyapunov (es)
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Krylov methods have been successfully used to solve large matrix equations with sparse coefficients. In this paper, we are interested on solving the low-rank Lyapunov equation whether in the continuous or discrete case. We propose to modify the block Arnoldi process so that the projection Krylov subspace contains some additional blocks that involves the inverse of the square coefficient of this equation. Our goal with this approach is to reduce the number of iterations and convergence time required by the classical block Arnoldi method. To show the effectiveness of the proposed method, some numerical experiments are carried out.
Los métodos de Krylov se han utilizado para resolver ecuaciones matriciales de gran tamaño con coeficientes dispersos. Este artículo se centra en la resolución de la ecuación de Lyapunov de rango bajo, tanto en el caso continuo como en el discreto. Se modifica el proceso de Arnoldi por bloques de manera que el subespacio de proyección de Krylov involucre bloques adicionales que incorporen la inversa del coeficiente cuadrático de dicha ecuación. El objetivo de este forma de atacar el problema es reducir el número de iteraciones y con ello el tiempo de convergencia que requiere el método clásico de Arnoldi por bloques. Para mostrar la eficacia del método propuesto, se incluyen varios experimentos numéricos.
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