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Efficient initials for computing maximal eigenpair

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Abstract

This paper introduces some efficient initials for a well-known algorithm (an inverse iteration) for computing the maximal eigenpair of a class of real matrices. The initials not only avoid the collapse of the algorithm but are also unexpectedly efficient. The initials presented here are based on our analytic estimates of the maximal eigenvalue and a mimic of its eigenvector for many years of accumulation in the study of stochastic stability speed. In parallel, the same problem for computing the next to the maximal eigenpair is also studied.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems (Beijing Normal University), Ministry of Education, Beijing, 100875, China

    Mu-Fa Chen

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  1. Mu-Fa Chen
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Correspondence to Mu-Fa Chen.

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Chen, MF. Efficient initials for computing maximal eigenpair. Front. Math. China 11, 1379–1418 (2016). https://doi.org/10.1007/s11464-016-0573-4

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  • DOI: https://doi.org/10.1007/s11464-016-0573-4

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