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Thanks for mentioning that. It's a problem I occasionally need to solve and based on your comment, I found this helpful write up by Nick Higham [1].

[1] https://nhigham.com/2021/01/26/what-is-the-nearest-positive-...




In my case, I am applying this in the calibration of instantaneous correlation matrices. His relevant papers can be found at [0]. It was really helpful that he also published MATLAB code of most of his algorithms.

[0] https://nhigham.com/correlation-matrices/




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