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On error bounds for systems

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Abstract

In this paper we discuss some conditions ensuring the error bound property for a family of functions. By virtual of matrix theory on strongly positive matrices we provide some descent/directional descent conditions ensuring the existence of error bounds for systems of functions. These conditions relax the descent requirement for functions and provide useful methods for establishing error bounds.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (Project Nos. 11371173, and 11301222), Earmarked Grants (GRF) from the Research Grant Council of Hong Kong (Project Nos. CUHK 402612, and 14304014), and Natural Science Foundation of Guangdong Province, China (Project Nos. S2012040007333, and S2012040007860). The authors thank Professor C. C. Chou for the stimulating discussion and valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Jinan University, Guangzhou, 510632, People’s Republic of China

    C. G. Liu

  2. Department of Mathematics, Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong

    K. F. Ng

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  1. C. G. Liu
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  2. K. F. Ng
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Correspondence to C. G. Liu.

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Liu, C.G., Ng, K.F. On error bounds for systems. TOP 23, 552–566 (2015). https://doi.org/10.1007/s11750-014-0353-9

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  • DOI: https://doi.org/10.1007/s11750-014-0353-9

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