Numerical Splitting Schemes as the Cornerstone for Mini-Batch Optimization: On the Importance of Well-Balanced Methods
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@ssrn.bsky.socialThis paper replaces expensive matrix-exponential calculations in Fokker-Planck equations with rational approximations, delivering similar accuracy while running 10-32× faster in benchmark tests. spkl.io/633277RzBb
![Table 2. Positivity thresholds on a sinh-stretched mesh, x = csinhξ with ξ uniform, for the Ornstein Uhlenbeck operator Eq. (24) with κ = σ = 1 on [−6,6] at fixed n = 161; smaller c gives stronger grading. The weighted column sum Eq. (15) holds to round-off at every stretching, and the negative off-diagonal entries remain confined to the bands ±2, so the operator remains EM. Across the sweep, τ0 increases by a factor of 2.4 and γ0 by 4.2, whereas γr changes by only 0.6%](https://cdn.bsky.app/img/feed_fullsize/plain/did:plc:2peq6vdr5mx2qrvf6ff5jqg2/bafkreib2alxjfilaqsfwu6zjpjd6w3sdo4522wsgesxoapu4did4vsbvoi@jpeg)