Showing math.NAShow all
3 papers · 1 filter
math.NA2026
Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning
Ronald Katende
We develop a non-asymptotic approximation, sampling, and finite-iteration optimization theory for variational physics-informed approximation of uniformly monotone nonlinear multisc…
math.NA2026
No-Harm Physics-Informed Inverse Learning with Residual-Calibrated Uncertainty
Ronald Katende
Physics-informed learning is increasingly used for partial differential equation (PDE)-governed inverse problems, but its reliability remains difficult to certify. This paper devel…
math.NA2025
Preserving Extreme Singular Values with One Oblivious Sketch
John M. Mango, Ronald Katende
We study when a single linear sketch can control the largest and smallest nonzero singular values of every rank- matrix. Classical oblivious embeddings require $s=Î(r/\varepsil…