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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