منابع مشابه
Lazy Householder Decomposition of Sparse Matrices
This paper describes Householder reduction of a rectangular sparse matrix to small band upper triangular form Bk+1. Bk+1 is upper triangular with nonzero entries only on the diagonal and on the nearest k superdiagonals. The algorithm is similar to the Householder reduction used as part of the standard dense SVD computation. For the sparse “lazy” algorithm, matrix updates are deferred until a ro...
متن کاملThe CORDIC Householder algorithm
A novel n-dimensional (n-D) CORDIC algorithm. for Euclidean and pseudo-ELclidian rotations,% proposed. The new algorithm is closely related to Householder transformations. It is shown to converge faster than CORDIC algorithms developed earlier for n = 3 and 4. Processor architectures for the algorithm are presented. The area and time performance of n-D CORDIC processors are evaluated. For a com...
متن کاملThe Householder - QL Matrix Diagonalisation
In this paper we report an eeective parallelisation of the House-holder routine for the reduction of a real symmetric matrix to tri-diagonal form and the QL algorithm for the diagonalisation of the resulting matrix. The Householder algorithm scales like N 3 =P + N 2 log 2 (P) and the QL algorithm like N 2 + N 3 =P as the number of processors P is increased for xed problem size. The constant par...
متن کاملCharacteristic properties of Mueller matrices. J. J. Gil
A complete and minimum set of necessary and sufficient conditions for a real 4x4 matrix to be a physical Mueller matrix is obtained. An additional condition is presented to complete the set of known conditions, namely the four conditions obtained from the non-negativity of the eigenvalues of the Hermitian matrix H associated with a Mueller matrix M and the Transmittance Condition. Using the pro...
متن کاملNonnegative Diagonals and High Performance on Low-Profile Matrices from Householder QR
The Householder reflections used in LAPACK’s QR factorization leave positive and negative real entries along R’s diagonal. This is sufficient for most applications of QR factorizations, but a few require that R have a non-negative diagonal. This note provides a new Householder generation routine to produce a non-negative diagonal. Additionally, we find that scanning for trailing zeros in the ge...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2012
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.08.002