Computational Mathematics Research Digest · Issue 2
Coverage: substantive postings from 13–20 August 2026. Four core selections and one strategic cross-disciplinary read.
Why it matters
A rescaling of Gaussian or hashing Johnson–Lindenstrauss matrices improves evaluation complexity from O(pn²ε−2) to O(pnε−2) without redesigning the underlying random-subspace model-based DFO method.
Read first
Section 2.2, particularly Corollary 2.4 and Remark 2.5, for why Q=Sᵀ/√n removes an entire factor of n and why further scaling does not improve the asymptotic result.
Why it matters
The infeasible interior-point method avoids nested outer–inner solution for constrained quadratic min–max problems, following a single central path and targeting nondegenerate stationary points.
Read first
Sections 2.3–2.5 for stationarity, Algorithm 1 in Section 3.2, and Sections 4.3–4.5 for scaling, coupled-constraint, and min-cost-flow tests.
Why it matters
PANDA combines proximal quasi-Newton iterations with adaptive steps and a matrix-free sensitivity calculation using implicit differentiation, automatic-differentiation products, and MINRES. Reported trailer-control tests show substantial forward, backward, and memory improvements.
Read first
Algorithm 1 and Section 3.2 for the forward/backward construction, then Figure 3 and Table 1. Broader benchmarking beyond the demonstrated NMPC family remains desirable.
Why it matters
The method targets ill-conditioned nonlinear parameter estimation with confounded parameters and heteroscedastic or serially correlated residuals. It updates the ridge parameter automatically within iterative generalized least squares.
Read first
Section 5 for the BIC/AICc hyperparameter fixed-point formulas, Section 6 for the full procedure, and Section 7’s battery state-of-health simulation.
Why it matters
A differentiable reformulation, Sinkhorn iterations, implicit differentiation, and GPU optimization lead to the certified bound ω<2.371177, illustrating numerical optimization’s contribution to linear-algebra complexity theory.
Read first
Section 3 for the optimization machinery and Section 4 for the exact-rational certification that converts a floating-point candidate into a rigorous result.
Selection and commentary are editorial. Dates and bibliographic details link to the cited primary sources.