algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of an orthonormal...

and, if appropriate, QR decomposition, this forms the DGESVD routine for the computation of the singular value decomposition. The QR algorithm can also...

linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃəˈlɛski/ shə-LES-kee) is a decomposition of a Hermitian, positive-definite...

QR decomposition is numerically stable. Traditionally applicable to: square matrix A, although rectangular matrices can be applicable. Decomposition:...

alternate between the QR decomposition and the LQ decomposition to find the real diagonal Hermitian matrices. The QR decomposition gives ⁠ M ⇒ Q R {\displaystyle...

pounds avoirdupois QR decomposition, a decomposition of a matrix QR algorithm, an eigenvalue algorithm to perform QR decomposition Quadratic reciprocity...

complex vector x into a complex multiple of a complex vector e. For the QR decomposition, e will be a unit coordinate vector, say for the kth coordinate. A...

ULV decomposition or URV decomposition, respectively. The UTV decomposition is usually computed by means of a pair of QR decompositions: one QR decomposition...

a product of an orthogonal matrix and an upper triangular matrix (QR decomposition, a consequence of Gram–Schmidt orthogonalization). It is named after...

the column vectors of a full column rank matrix yields the QR decomposition (it is decomposed into an orthogonal and a triangular matrix). The vector projection...

an orthogonal decomposition; the QR decomposition will serve to illustrate the process. J = Q R {\displaystyle \mathbf {J} =\mathbf {QR} } where Q is...

decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix decomposition)...

important matrix decompositions (Golub & Van Loan 1996) involve orthogonal matrices, including especially: QR decomposition M = QR, Q orthogonal, R upper...

discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one to write an arbitrary...

numerical accuracy, using the QR factorization of A to solve the least squares problem is preferred. The QR decomposition of a (tall) matrix A {\displaystyle...

An RRQR factorization or rank-revealing QR factorization is a matrix decomposition algorithm based on the QR factorization which can be used to determine...

overall residual. In particular if we take the QR decomposition of V 1 N − 1 = Q R {\displaystyle V_{1}^{N-1}=QR} , then a = R − 1 Q T v N {\displaystyle a=R^{-1}Q^{T}v_{N}}...

axes. The polar decomposition of a square matrix A {\displaystyle A} always exists. If A {\displaystyle A} is invertible, the decomposition is unique, and...

decomposition (SVD), but there are other less computationally expensive choices, such as QR decomposition with pivoting (so-called rank-revealing QR factorization)...

Hankel matrix (0,1)-matrix Matrix decomposition Cholesky decomposition LU decomposition QR decomposition Polar decomposition Reducing subspace Spectral theorem...

Cholesky decomposition may be computed without forming ⁠ A ∗ A {\displaystyle A^{*}A} ⁠ explicitly, by alternatively using the QR decomposition of A = Q...

coefficients. This effect can, for example, be employed for computing the QR decomposition of a matrix. One advantage over Householder transformations is that...

numerical linear algebra, we convert M to an orthogonal matrix, Q, using QR decomposition. However, we often prefer a Q closest to M, which this method does...

which can be solved by standard methods including QR decomposition and singular value decomposition, possibly including regularization techniques to deal...

factorized is a normal or real symmetric matrix, the decomposition is called "spectral decomposition", derived from the spectral theorem. A (nonzero) vector...

Philip A. (May 1995). "Fast rectangular matrix multiplication and QR decomposition". Linear Algebra and its Applications. 221: 69–81. doi:10.1016/0024-3795(93)00230-w...

{\beta }}}.} The matrix X is subjected to an orthogonal decomposition, e.g., the QR decomposition as follows. X = Q ( R 0 )   {\displaystyle...

orthogonal similarity transforms, somewhat like a two-sided QR decomposition. (For QR decomposition, the Householder rotations are multiplied only on the left...

are referred to as decomposition methods. Examples include the LU decomposition, the QR decomposition or the Cholesky decomposition (for positive definite...

n+1 equations for n unknowns. The minimum can be computed using a QR decomposition: find an (n + 1)-by-(n + 1) orthogonal matrix Ωn and an (n + 1)-by-n...