QR Decomposition
QR decomposition factors a matrix A into the product of an orthogonal matrix Q and an upper-triangular matrix R, A=QR, used for least squares and eigenvalues.
Purpose
To solve least-squares problems and compute eigenvalues with the QR algorithm.
Mechanism
Implemented via Gram-Schmidt, Householder reflections, or Givens rotations. Least squares Ax≈b becomes Rx=Q^T b (an upper-triangular system). Householder is the most numerically stable.
Use cases
- Least squares
- Eigenvalue computation
- Numerical linear algebra