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The Cartographer
A remark on approximating permanents of positive definite matrices
May 13, 2020 Β· Declared Dead Β· π Linear Algebra and its Applications
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Authors
Alexander Barvinok
arXiv ID
2005.06344
Category
cs.DS: Data Structures & Algorithms
Cross-listed
math.CO
Citations
3
Venue
Linear Algebra and its Applications
Last Checked
4 months ago
Abstract
Let $A$ be an $n \times n$ positive definite Hermitian matrix with all eigenvalues between 1 and 2. We represent the permanent of $A$ as the integral of some explicit log-concave function on ${\Bbb R}^{2n}$. Consequently, there is a fully polynomial randomized approximation scheme (FPRAS) for the permanent of $A$.
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