# Keyword : QR

 F02WDF $QR$ factorization, possibly followed by SVD F06QPF $QR$ factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix F06QQF $QR$ factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row F06QRF $QR$ or $RQ$ factorization by sequence of plane rotations, real upper Hessenberg matrix F06QSF $QR$ or $RQ$ factorization by sequence of plane rotations, real upper spiked matrix F06QTF $QR$ factorization of $UP$ or $RQ$ factorization of $PU$, $U$ real upper triangular, $P$ a sequence of plane rotations F06TPF $QR$ factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix F06TRF $QR$ or $RQ$ factorization by sequence of plane rotations, complex upper Hessenberg matrix F06TSF $QR$ or $RQ$ factorization by sequence of plane rotations, complex upper spiked matrix F06TTF $QR$ factorization of $UP$ or $RQ$ factorization of $PU$, $U$ complex upper triangular, $P$ a sequence of plane rotations F08AEF $QR$ factorization of real general rectangular matrix F08AFF Form all or part of orthogonal $Q$ from $QR$ factorization determined by F08AEF, F08BEF or F08BFF F08AGF Apply orthogonal transformation determined by F08AEF, F08BEF or F08BFF F08ASF $QR$ factorization of complex general rectangular matrix F08ATF Form all or part of unitary $Q$ from $QR$ factorization determined by F08ASF, F08BSF or F08BTF F08AUF Apply unitary transformation determined by F08ASF, F08BSF or F08BTF F08BEF $QR$ factorization of real general rectangular matrix with column pivoting F08BFF $QR$ factorization of real general rectangular matrix with column pivoting, using BLAS-3 F08BSF $QR$ factorization of complex general rectangular matrix with column pivoting F08BTF $QR$ factorization of complex general rectangular matrix with column pivoting, using BLAS-3 F08JEF All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit $QL$ or $QR$ algorithm F08JFF All eigenvalues of real symmetric tridiagonal matrix, root-free variant of the $QL$ or $QR$ algorithm F08JSF All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit $QL$ or $QR$ algorithm F08ZEF Computes a generalized $QR$ factorization of a real matrix pair F08ZSF Computes a generalized $QR$ factorization of a complex matrix pair

© The Numerical Algorithms Group Ltd, Oxford UK. 2013