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Exact inverse solution techniques for a class of complex valued block two-by-two linear systems

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Abstract

By taking a complex factorization of the Schur complement matrix into consideration, we present practical expressions for the inverses of a class of complex valued block two-by-two matrices. Then, based on the obtained practical inverse expressions, some efficient exact inverse solution methods are presented for solving the related linear systems within both iterative refinement and Krylov subspace accelerations. Numerical experiments indicate that in most cases the proposed exact inverse methods perform better than the MINRES and GMRES methods accelerated by some existing efficient preconditioners.

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Funding

This work was supported by the National Natural Science Foundation of China (Nos. 11901267, 11801242 and 11771193) and the Ministry of Education, Youth and Sports of the Czech Republic from the National Programme of Sustainability (NPU II), project “IT4Innovations excellence in science–LQ1602.”

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Correspondence to Zhao-Zheng Liang.

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Liang, ZZ., Axelsson, O. Exact inverse solution techniques for a class of complex valued block two-by-two linear systems. Numer Algor 90, 79–98 (2022). https://doi.org/10.1007/s11075-021-01180-z

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  • DOI: https://doi.org/10.1007/s11075-021-01180-z

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