In linear 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 matrix Q and an upper triangular matrix R. QR decomposition is often used to solve the linear least squares (LLS) problem and is the basis for a particular eigenvalue algorithm, the QR algorithm.
algebra, a QRdecomposition, 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, QRdecomposition, 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...
QRdecomposition is numerically stable. Traditionally applicable to: square matrix A, although rectangular matrices can be applicable. Decomposition:...
alternate between the QRdecomposition and the LQ decomposition to find the real diagonal Hermitian matrices. The QRdecomposition gives M ⇒ Q R {\displaystyle...
pounds avoirdupois QRdecomposition, a decomposition of a matrix QR algorithm, an eigenvalue algorithm to perform QRdecomposition Quadratic reciprocity...
complex vector x into a complex multiple of a complex vector e. For the QRdecomposition, 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 QRdecompositions: one QR decomposition...
decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix decomposition)...
a product of an orthogonal matrix and an upper triangular matrix (QRdecomposition, a consequence of Gram–Schmidt orthogonalization). It is named after...
important matrix decompositions (Golub & Van Loan 1996) involve orthogonal matrices, including especially: QRdecomposition 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...
axes. The polar decomposition of a square matrix A {\displaystyle A} always exists. If A {\displaystyle A} is invertible, the decomposition is unique, and...
An RRQR factorization or rank-revealing QR factorization is a matrix decomposition algorithm based on the QR factorization which can be used to determine...
which can be solved by standard methods including QRdecomposition and singular value decomposition, possibly including regularization techniques to deal...
numerical accuracy, using the QR factorization of A to solve the least squares problem is preferred. The QRdecomposition of a (tall) matrix A {\displaystyle...
coefficients. This effect can, for example, be employed for computing the QRdecomposition of a matrix. One advantage over Householder transformations is that...
overall residual. In particular if we take the QRdecomposition 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}}...
numerical linear algebra include obtaining matrix decompositions like the singular value decomposition, the QR factorization, the LU factorization, or the eigendecomposition...
numerical linear algebra, we convert M to an orthogonal matrix, Q, using QRdecomposition. However, we often prefer a Q closest to M, which this method does...
orthogonal similarity transforms, somewhat like a two-sided QRdecomposition. (For QRdecomposition, the Householder rotations are multiplied only on the left...
Philip A. (May 1995). "Fast rectangular matrix multiplication and QRdecomposition". Linear Algebra and its Applications. 221: 69–81. doi:10.1016/0024-3795(93)00230-w...
matrix decomposition are Gaussian elimination, LU decomposition, Cholesky decomposition for symmetric (or hermitian) and positive-definite matrix, and QR decomposition...
factorized is a normal or real symmetric matrix, the decomposition is called "spectral decomposition", derived from the spectral theorem. A (nonzero) vector...
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