QRrozklad
QRrozklad (Polish: rozkład QR) is a matrix factorization that expresses an m-by-n matrix A as A = Q R, where Q has orthonormal columns and R is upper triangular (for m ≥ n). When using the reduced or economy form, A = Q_r R with Q_r of size m×n and R of size n×n. The factorization is widely used to solve linear least squares problems and to simplify eigenvalue computations.
Computationally, QRrozklad can be obtained by Gram-Schmidt orthogonalization (classical but numerically sensitive), modified Gram-Schmidt, or more
Complexity for an m×n matrix with m ≥ n is about O(m n^2). Reduced QR is used when
In practice, QRrozklad is a standard tool in numerical linear algebra, data analysis, and scientific computing.