LU Decomposition and Iterative Methods (Jacobi and Gauss-Seidel)
Beyond the basics: what computers do when the system has a million unknowns instead of three.
What this unit covers
Unit 4: Solution of Systems of Linear Equations
- 1 Augmented Matrices and Elementary Row OperationsFrom equations to a grid of numbers: strip away the letters, and three simple row moves do all the work. · 4 min
- 2 Gaussian Elimination with Back SubstitutionMake zeros, build a staircase, then walk back up it one unknown at a time. · 7 min
- 3 Row Echelon Form and the Row Echelon MethodThat staircase shape has a precise definition — learn three rules and you'll spot row echelon form at a glance. · 4 min
- 4 Gauss-Jordan EliminationDon't stop at the staircase — keep clearing until the solution reads itself straight off the last column. · 5 min
- 5 LU Decomposition and Iterative Methods (Jacobi and Gauss-Seidel)Beyond the basics: what computers do when the system has a million unknowns instead of three. · 8 min