Hybrid Ikebe–Newton’s iteration for inverting general nonsingular Hessenberg matrices

J. Abderramán Marrero and M. Rachidi

Applied Mathematics and Computation, 2015, vol. 268, issue C, 413-421

Abstract: After a concise survey, the expanded Ikebe algorithm for inverting the lower half plus the superdiagonal of an n × n unreduced upper Hessenberg matrix H is extended to general nonsingular upper Hessenberg matrices by computing, in the reduced case, a block diagonal form of the factor matrix HL in the inverse factorization H−1=HLU−1. This factorization enables us to propose hybrid and accurate (nongaussian) procedures for computing H−1. Thus, HL is computed directly in the aim to be used as a fine initial guess for Newton’s iteration, which converges to H−1 in a suitable number of iterations.

Keywords: Accuracy; Hessenberg matrix; Matrix inverse; Newton’s method (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:268:y:2015:i:c:p:413-421

DOI: 10.1016/j.amc.2015.06.084

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