Abstract
This paper focuses on algorithms for the truncated Takagi factorization of complex symmetric matrices. The problem is formulated as a Riemannian optimization problem on a complex Stiefel manifold and then is converted into a real Riemannian optimization problem on the intersection of the real Stiefel manifold and the quasi-symplectic set. The steepest descent, the Riemannian nonmonotone conjugate gradient, Newton, and hybrid methods are used for solving the problem and they are compared in their performance for the optimization task. Numerical experiments are provided to illustrate the efficiency of the proposed method.
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The data and code that support the findings of this study are available from the first author upon reasonable request.
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Acknowledgements
The authors thank the anonymous referees for their helpful comments and valuable suggestions.
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**ao Shan Chen is supported by the National Science Foundation of China under Grant numbers 11771159, as well as the Guangdong Provincial Natural Science Foundation under project number 2022A1515011123.
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Both authors wrote the main manuscript text. Ling Chang Kong performed the experiment. **ao Shan Chen contributed to the conception of the study and helped to improve this manuscript with constructive suggestions. Both authors reviewed the manuscript.
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Kong, L.C., Chen, X.S. Riemannian optimization methods for the truncated Takagi factorization. Numer Algor (2023). https://doi.org/10.1007/s11075-023-01701-y
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DOI: https://doi.org/10.1007/s11075-023-01701-y