Methods Archive
Numerical Analysis Algorithm Library
Solving Equations
Gaussian Elimination & LU Decomposition
From pivoting to LU decomposition and sparse matrix processing. A deep dive into core algorithms for solving linear systems efficiently.
Newton's Method
The most essential algorithm in numerical analysis for iteratively solving systems of nonlinear equations using the Jacobian matrix.
Homotopy Method
A robust algorithm for global convergence through path-tracking. Overcoming initial value dependency with Arc-length continuation.
Optimization & Data Fitting
Simplex Method
An algorithm for finding the optimal solution to Linear Programming (LP) problems by traversing the vertices of the feasible region. Explains slack variables and pivot operations.
Interior Point Method
An algorithm that traverses the interior of the feasible region along the 'Central Path' to reach the optimum. Explains the Primal-Dual Path Following Method and Newton's equation derivation.
Least Squares Method
The mathematics of polynomial approximation using the least squares method. Explores the process of deriving normal equations from discrete data and solving systems of linear equations via LU decomposition.
Genetic Algorithm
An optimization method that evolves candidates through selection, crossover, and mutation. Illustrated with a step-by-step flow and a population plot.
Numerical Integration & Stochastic Methods
Numerical Integration
Addressing the stability-accuracy tradeoff for Stiff ODEs. Deep dive into Trapezoidal and GEAR (BDF) methods.
Monte Carlo Method
Mathematics and practice of the Monte Carlo method. Explores yield simulation due to component tolerance and global optimization algorithms for solving nonlinear equations using random numbers.