Refines the solution of a system of linear equations with a general coefficient matrix and estimates its error.
Estimates the error in the solution of a system of linear equations with a triangular coefficient matrix.
Computes the inverse of a triangular matrix.
Computes the solution to the system of linear equations with a square coefficient matrix A and multiple right-hand sides, and provides error bounds on the solution.
Uses factorization to compute the solution to the system of linear equations with a symmetric (Hermitian) positive definite tridiagonal coefficient matrix A, and provides error bounds on the solution.
This topic describes the LAPACK routines for the QR (RQ) and LQ (QL) factorization of matrices. Routines for the RZ factorization as well as for generalized QR and RQ factorizations are also included.
QR Factorization. Assume that A is an m-by-n matrix to be factored.
If m≥n, the QR factorization is given by
Computes the QL factorization of a general m-by-n matrix.
Applies a real or complex orthogonal matrix obtained from a "triangular-pentagonal" complex block reflector to a general real or complex matrix, which consists of two blocks.
Multiplies a complex matrix by the complex unitary matrix Q determined by ?hetrd.
Computes the eigenvectors corresponding to specified eigenvalues of a real symmetric tridiagonal matrix.