Articles

Secant Method 🇺🇸

September 21, 2026
Category: Numerical Methods

The Secant Method is a root-finding algorithm used in numerical analysis to approximate the zeros of a given function $f(x)$. It can be regarded as a derivative-free variant of Newton's method. Instead of computing the derivative $f'(x)$ at each iteration (as done in Newton’s method), it approximate...

Relaxation Method 🇺🇸

September 21, 2026
Category: Numerical Methods

The relaxation method, commonly referred to as the fixed-point iteration method, is an iterative approach used to find solutions (roots) to nonlinear equations of the form $f(x) = 0$. Instead of directly solving for the root, the method involves rewriting the original equation in the form...

Newtons Method 🇺🇸

September 21, 2026
Category: Numerical Methods

Newton's method (or the Newton-Raphson method) is a powerful root-finding algorithm that exploits both the value of a function and its first derivative to rapidly refine approximations to its roots. Unlike bracketing methods that work by enclosing a root between two points, Newton's method is an ope...

Golden Ratio Search 🇺🇸

September 21, 2026
Category: Numerical Methods

The Golden Ratio Search is a technique employed for locating the extremum (minimum or maximum) of a unimodal function over a given interval. Unlike gradient-based or derivative-requiring methods, this approach uses only function evaluations, making it broadly applicable even when derivatives are dif...

Gradient Descent 🇺🇸

September 21, 2026
Category: Numerical Methods

Gradient Descent is a fundamental first-order optimization algorithm widely used in mathematics, statistics, machine learning, and artificial intelligence. Its principal aim is to find the minimum of a given differentiable function $f(x)$. Instead of searching blindly, it uses gradient information —...

Bisection Method 🇺🇸

September 21, 2026
Category: Numerical Methods

The bisection method is a classical root-finding technique used extensively in numerical analysis to locate a root of a continuous function $f(x)$ within a specified interval $[a, b]$. It belongs to the family of bracketing methods, which use intervals known to contain a root and systematically redu...

Root Finding 🇺🇸

September 21, 2026
Category: Numerical Methods

Root-finding algorithms aim to solve equations of the form...

Taylor Series 🇺🇸

September 21, 2026
Category: Numerical Methods

The Taylor series is a fundamental tool in calculus and mathematical analysis, offering a powerful way to represent and approximate functions. By expanding a function around a specific point, known as the "center" or "point of expansion," we can express it as an infinite sum of polynomial terms deri...

Differentiation 🇺🇸

September 21, 2026
Category: Numerical Methods

Differentiation is a cornerstone concept in calculus, fundamental to understanding how quantities change in relation to one another. At its core, differentiation is used to determine the rate at which a particular quantity is changing at a specific point. This rate of change is quantitatively expres...

Central Difference 🇺🇸

September 21, 2026
Category: Numerical Methods

The central‐difference method is a finite‐difference scheme for estimating derivatives that combines forward and backward differences via Taylor‐series expansions. By evaluating the function at points symmetrically placed around the target, it cancels out many of the lower‐order error terms, yieldin...

Thin Plate Spline Interpolation 🇺🇸

September 21, 2026
Category: Numerical Methods

Thin-plate spline (TPS) interpolation is a smooth method for fitting a surface through scattered points in two or more dimensions...

Interpolation 🇺🇸

September 21, 2026
Category: Numerical Methods

Interpolation constructs a function that passes exactly through a set of known data points. If the data are...

Gaussian Interpolation 🇺🇸

September 21, 2026
Category: Numerical Methods

Gaussian radial basis function (RBF) interpolation builds a smooth interpolant from Gaussian functions centered at the data sites...

Cubic Spline Interpolation 🇺🇸

September 21, 2026
Category: Numerical Methods

A cubic spline interpolates data with a sequence of cubic polynomials rather than one high-degree polynomial across the entire interval...

Least Squares 🇺🇸

September 21, 2026
Category: Numerical Methods

Least squares fits a model to data by minimizing the sum of squared residuals...

Linear Interpolation 🇺🇸

September 21, 2026
Category: Numerical Methods

Linear interpolation estimates a value between two known points by assuming the function is a straight line over that interval...

Newton Polynomial 🇺🇸

September 21, 2026
Category: Numerical Methods

Newton interpolation represents the same unique polynomial obtained by Lagrange interpolation, but in a form that is easier to build incrementally...

Regression 🇺🇸

September 21, 2026
Category: Numerical Methods

Regression models the relationship between one or more predictors and a response variable. Unlike interpolation, regression generally does not try to pass exactly through every observation. Instead, it chooses model parameters that balance data fit with a chosen model structure...

Lagrange Polynomial Interpolation 🇺🇸

September 21, 2026
Category: Numerical Methods

Lagrange interpolation constructs the unique polynomial of degree at most $n$ that passes through $n+1$ distinct data points...

Mission Startup 🇺🇸

September 19, 2026
Category: Standard Of Iron

Mission startup separates preparation from playable simulation. Loading a battle is not one monolithic map parse: the application resolves the authored map, constructs the world, applies mission ownership/setup, initializes AI, prepares renderer-facing terrain/scatter state, starts simulation, and k...

Horse Model Architecture 🇺🇸

September 19, 2026
Category: Standard Of Iron

Horses and elephants use authored, skinned low-poly geometry compiled into deterministic creature packages. The production pipeline preserves mesh topology, skinning weights, joint hierarchy, authored animation channels, attachment landmarks, and reviewed production proportions from asset generation...

Audio System 🇺🇸

September 19, 2026
Category: Standard Of Iron

Everything the player hears goes through one path: a cue is requested by gameplay or QML, the cue registry picks a resource from the manifest, AudioSystem decides whether it may play, and the miniaudio backend mixes it. Music and ambience beds are chosen by tags in the manifest rather than by ID in ...

Ambient Wildlife 🇺🇸

September 16, 2026
Category: Standard Of Iron

Ambient wildlife makes battlefields feel inhabited rather than staged. Sheep occupy pasture, wolves work the edges of settlement and cover, and bird flocks move through the sky or burst away from nearby threats...

Food and Farms 🇺🇸

September 15, 2026
Category: Standard Of Iron

Food connects settlement growth to military production. Farms grow grain, builders harvest grain or slaughter sheep, homes spend food to recruit civilians, and civilians become manpower when they reach a barracks. The result is an economic loop in which food drives population while wood, stone, and ...

Minimap 🇺🇸

September 14, 2026
Category: Standard Of Iron

The HUD minimap combines four cached raster layers with one live QML overlay. The split is designed around invalidation: stable pictures of world state are rebuilt only when their inputs change, while continuously animated signals stay on the scene graph...

Animation Architecture 🇺🇸

September 14, 2026
Category: Standard Of Iron

How a creature in Standard of Iron goes from "this unit is attacking" to moving geometry on screen — and why it is fast enough to do for thousands of units at once...

Save Load System 🇺🇸

September 14, 2026
Category: Standard Of Iron

Standard of Iron stores match saves in a versioned SQLite database. A save is more than a serialized entity list: it combines the authoritative battlefield, non-entity session state, campaign/mission metadata, and a preview image, then stores that snapshot with compression, checksums, transactional ...

Stationarity 🇺🇸

September 14, 2026
Category: Statistics Notes

Stationarity describes which probabilistic features of a time series remain stable when the time origin is shifted. Weak stationarity focuses on a constant mean and variance together with an autocovariance that depends only on lag, while strict stationarity requires the full joint distribution to be...

Forecast Evaluation 🇺🇸

September 14, 2026
Category: Statistics Notes

Forecast evaluation measures how an entire forecasting procedure performs on observations that were genuinely unknown when each prediction was made. It is therefore different from in-sample fit: transformations, feature construction, parameter estimation, predictor values, and model selection all ha...

Autoregressive Models 🇺🇸

September 14, 2026
Category: Statistics Notes

Autoregressive models describe a time series whose current value depends linearly on its own recent history plus a new innovation. The lag coefficients determine how strongly past observations persist into the present and whether the process tends to decay smoothly, alternate, or oscillate...

Frequency Domain Analysis 🇺🇸

September 14, 2026
Category: Statistics Notes

Frequency-domain analysis describes a time series by the cycle lengths that contribute to its variation rather than by relationships at individual lags. The periodogram and spectral density provide a complementary view to the ACF, translating repeated temporal structure into peaks at corresponding f...

Stochastic Processes and White Noise 🇺🇸

September 14, 2026
Category: Statistics Notes

A stochastic process is a collection of random variables indexed by time, and an observed time series is one realized path from that process. This viewpoint separates the data we actually see from the probabilistic mechanism used to describe possible paths and future uncertainty...

Dynamic Regression 🇺🇸

September 14, 2026
Category: Statistics Notes

Dynamic regression combines external predictors with time-series structure so that the conditional mean can respond to explanatory variables without assuming the remaining errors are independent. Lagged predictors can represent delayed effects, while ARMA or ARIMA errors capture serial dependence le...

Invertibility 🇺🇸

September 14, 2026
Category: Statistics Notes

Invertibility is the condition that lets a moving-average or ARMA model recover its unobserved innovations from the observed series in a stable way. It turns the shock representation of the model into a usable past-based filter whose coefficients decay rather than grow without bound...

Multivariate Time Series 🇺🇸

September 14, 2026
Category: Statistics Notes

Multivariate time-series models describe several evolving variables jointly so that cross-lag feedback, shared shocks, and predictive relationships can be represented within one system. They are useful when separate univariate models would ignore information carried by the histories of related serie...