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Numerical methods for solving some matrix feasibility problems

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Abstract

In this paper, we design two numerical methods for solving some matrix feasibility problems, which arise in the quantum information science. By making use of the structured properties of linear constraints and the minimization theorem of symmetric matrix on manifold, the projection formulas of a matrix onto the feasible sets are given, and then the relaxed alternating projection algorithm and alternating projection algorithm on manifolds are designed to solve these problems. Numerical examples show that the new methods are feasible and effective.

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Authors and Affiliations

  1. College of Mathematics and Computational Science, Guangxi Colleges and Universities, Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin, 541004, People’s Republic of China

    Xue-Feng Duan, Chun-Mei Li & Jiao-Fen Li

  2. Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology, Guilin, 541004, People’s Republic of China

    Yong Ding

Authors
  1. Xue-Feng Duan
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  2. Chun-Mei Li
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  3. Jiao-Fen Li
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  4. Yong Ding
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Corresponding author

Correspondence to Xue-Feng Duan.

Additional information

The work was supported by the National Natural Science Foundation of China (No.11561015; 11261014; 11301107; 11361018), the Natural Science Foundation of Guangxi Province (No.2014GXNSFAA118004).

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Duan, XF., Li, CM., Li, JF. et al. Numerical methods for solving some matrix feasibility problems. Numer Algor 74, 461–479 (2017). https://doi.org/10.1007/s11075-016-0155-2

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  • DOI: https://doi.org/10.1007/s11075-016-0155-2

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