Qr Householder
Householder Reflections
To compute the QR factorization of an arbitrary (n x m)-matrix A with R=QA, where Q is a orthogonal matrix and R an upper triangle matrix, use the command B = QRHOUSE(A). The resulting matrix B contains in the upper triangle the matrix R and in each column the necessary information for the Householder vector v of the corresponding Householder. The more common approach to QR decomposition is employing Householder reflections rather than utilizing Gram-Schmidt. In practice, the Gram-Schmidt procedure is not recommended as it can lead to cancellation that causes inaccuracy of the computation of, which may result in a non-orthogonal matrix. This Householder QR decomposition is faster, but less numerically stable and less feature-full than FullPivHouseholderQR or ColPivHouseholderQR. This class supports the inplace decomposition mechanism.
QR Factorization Using Householder Transformations. Learn more about function q, r=qrfactor(a).
Eigen Householder Qr
Householder reflections and QR decomposition
- Keywords
- array
Usage
Arguments
- A
- numeric matrix with
nrow(A)>=ncol(A).
Details
The Householder method applies a succession of elementary unitary matrices to the left of matrix A. These matrices are the so-called Householder reflections.
Value
- List with two matrices
Q and R, Q orthonormal and R upper triangular, such that A=Q%*%R.References
Trefethen, L. N., and D. Bau III. (1997). Numerical Linear Algebra. SIAM, Society for Industrial and Applied Mathematics, Philadelphia.
See Also
Aliases
- householder