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Numerical Methods
Dec 18, 2023
ODE Foundations
26 min readOrdinary Differential Equations (11): Numerical Methods
From Euler's tangent step to Dormand-Prince adaptive integrators: a working numerics toolkit. Convergence orders, A-stability, stiffness, and when to reach for Radau or BDF instead of RK45.
Sep 22, 2022
Optimization Theory
24 min readOptimization (7): Second-Order Methods
Second-order methods break the sqrt(kappa) barrier by using curvature. We prove Newton's quadratic local convergence, derive BFGS from a secant condition + low-rank update, walk through L-BFGS's two-loop recursion that …