Methods Archive
Numerical Analysis Algorithm Library
01
Gaussian Elimination & LU Decomposition
From pivoting to LU decomposition and sparse matrix processing. A deep dive into core algorithms for solving linear systems efficiently.
Linear Algebra
02
Newton's Method
The most essential algorithm in numerical analysis for iteratively solving systems of nonlinear equations using the Jacobian matrix.
Nonlinear Solver
03
Homotopy Method
A robust algorithm for global convergence through path-tracking. Overcoming initial value dependency with Arc-length continuation.
Continuation Method
04
Numerical Integration
Addressing the stability-accuracy tradeoff for Stiff ODEs. Deep dive into Trapezoidal and GEAR (BDF) methods.
ODE Solver