Abstract
The nearest correlation matrix problem is to find a positive semidefinite matrix with unit diagonal, that is, nearest in the Frobenius norm to a given symmetric matrix A. This problem arises in the finance industry, where the correlations are between stocks. In this paper, we formulate this problem as a smooth unconstrained minimization problem, for which rapid convergence can be obtained. Other methods are also studied. Comparative numerical results are reported.
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S. Al-Homidan is grateful to King Fahd University of Petroleum and Minerals for providing excellent research facilities.
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Al-Homidan, S., AlQarni, M. Structure methods for solving the nearest correlation matrix problem. Positivity 16, 497–508 (2012). https://doi.org/10.1007/s11117-012-0180-x
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DOI: https://doi.org/10.1007/s11117-012-0180-x
Keywords
- Alternating projections method
- Correlation matrix
- Nearness problem
- Newton method
- Positive semidefinite programing
- Semidefinite matrix