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About this paper
Siavash Ameli, Chris van der Heide, Liam Hodgkinson, Michael W. Mahoney
Free decompression estimates a large Hermitian matrix’s spectrum from eigenvalues of a smaller principal submatrix. It fits a bivariate polynomial to the Stieltjes transform and evolves its spectral curve while tracking the physical root. In a diffusion-model test, a 4,000-dimensional fit reconstructed the 64,000-dimensional spectrum across a wide eigenvalue range, with full-matrix validation; the extreme left edge remains difficult.
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