Numerical Linear Algebra
The subfield of numerical analysis studying algorithms for performing matrix operations efficiently and accurately on digital computers.
Governing formula
LU: A = L U, QR: A = Q R, SVD: A = U Σ V^T
SI unit
Matrix Factorization Algorithms
In depth
Focuses on solving large sparse linear systems (A x = b), matrix inversion, and eigenvalue problems using factorizations (LU, Cholesky, QR, SVD) and iterative solvers (Conjugate Gradient, GMRES).
Examples in the real world
Solving 10-million-node finite element linear equations in structural and fluid dynamics simulations.