doi:10.1016/j.aml.2023.108778engDelgado, JorgePeña, GuillermoPeña, Juan ManuelAccurate and fast computations with Green matricesART-2023-134615This paper provides a linear time complexity method to obtain the bidiagonal decomposition of Green matrices with high relative accuracy. In addition, when the Green matrix is nonsingular and totally positive, this bidiagonal decomposition can be used to compute the eigenvalues, the inverse and the solution of some linear system of equations with high relative accuracy. A numerical example illustrates the advantages of this method.2023http://zaguan.unizar.es/record/12758710.1016/j.aml.2023.108778http://zaguan.unizar.es/record/127587oai:zaguan.unizar.es:127587info:eu-repo/grantAgreement/ES/DGA/E41-23Rinfo:eu-repo/grantAgreement/ES/DGA/S39-23Rinfo:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-096321-B-I00info:eu-repo/grantAgreement/ES/MICINN/PID2020-112773GB-I00info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-Tinfo:eu-repo/grantAgreement/ES/UZ-IBERCAJA/JIUZ-2022-CSJ-19APPLIED MATHEMATICS LETTERS 145 (2023), 108778 [5 pp.]by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess