Tag
stability
- Oct 18, 2026 The Bilinear Transform and Frequency Warping How mapping the analog frequency axis onto the unit circle produces a stable digital filter, why the cutoff moves, and how prewarping compensates for it. scientific computing
- Oct 9, 2026 Counting and Radix Sort: Choosing the Pass Count and the Digit Width How stable counting sort works in one linear pass, how LSD radix composes passes, and how digit width trades passes against counter size. algorithms
- Jun 27, 2026 Forward Error, Backward Error, and Condition Numbers Separating what the algorithm got wrong from what the problem amplifies, why the rounding model hands over a backward error for free, and how a small residual can still mean a wrong answer. scientific computing
- Jun 6, 2026 Insertion Sort and the Inversion Count That Predicts Its Runtime How the shift loop makes insertion sort cost exactly n plus the number of inversions, why that adaptivity matters more than the quadratic worst case, and what binary insertion does not fix. algorithms
- Aug 8, 2025 Merge Sort: Why Stability Survives the Merge and What the Buffer Costs The merge invariant that preserves equal-key order, the three places extra memory is required, and how natural runs turn the algorithm adaptive. algorithms
- Jul 14, 2025 Stability Limits of Explicit Integration in Dynamics Why forward Euler and Verlet diverge above a step size bound, where the bound comes from, and how a hair or cloth solver stays stable past the limit that breaks a rigid-body integrator. computer graphics
- May 30, 2025 Cluster Validity, Stability, and Choosing the Number of Clusters Internal indices measure geometry that a clustering may not assume, stability is not a consistent selector, and chance-corrected agreement between resampled partitions answers a narrower question than it appears to. machine learning
- Feb 25, 2024 The Parabolic Step Limit in Explicit Diffusion Schemes Why an explicit update of the heat equation requires a step proportional to the square of the mesh spacing, what the amplification analysis shows, and how implicit treatment removes the restriction. scientific computing
- Apr 6, 2023 Stiffness: When Explicit Steps Collapse What makes an initial value problem stiff, why an explicit method is forced to steps far below what accuracy requires, and how the Jacobian eigenvalues set the forced step. scientific computing