https://jongha-jeon-dev.github.io/standarderror/tags/numerical-analysis/Recent content in Numerical-Analysis on The Standard ErrorHugo -- 0.123.7en-gbThu, 03 Sep 2026 00:00:00 +0000https://jongha-jeon-dev.github.io/standarderror/lectures/numerical-analysis-1-step-size/Thu, 03 Sep 2026 00:00:00 +0000https://jongha-jeon-dev.github.io/standarderror/lectures/numerical-analysis-1-step-size/Gradient descent is forward Euler on the gradient flow, so the learning rate is a discretisation step with a stability limit — exactly 2/λ_max on a quadratic, and on a network 2.04 times larger than that formula says, because the curvature moves to meet whatever step you chose.https://jongha-jeon-dev.github.io/standarderror/lectures/numerical-analysis-2-gradient-check/Thu, 03 Sep 2026 00:00:00 +0000https://jongha-jeon-dev.github.io/standarderror/lectures/numerical-analysis-2-gradient-check/The error of a finite difference is a U in the step size, so a smaller step is not a safer one — and the step decides what your gradient check can see, by eight orders of magnitude in float64 and nine more once you change the precision. In bfloat16 a gradient 17% wrong passes at every step size.https://jongha-jeon-dev.github.io/standarderror/posts/why-my-integrator-exploded-at-355/Thu, 06 Aug 2026 00:00:00 +0000https://jongha-jeon-dev.github.io/standarderror/posts/why-my-integrator-exploded-at-355/Two silent numerical bugs, and the kind of test that actually catches them