A BLAS-3 Version of the QR Factorization with Column Pivoting
نویسندگان
چکیده
The QR factorization with column pivoting (QRP), originally suggested by Golub and Businger in 1965, is a popular approach to computing rank-revealing factorizations. Using BLAS Level 1, it was implemented in LINPACK, and, using BLAS Level 2, in LAPACK. While the BLAS Level 2 version delivers, in general, superior performance, it may result in worse performance for large matrix sizes due to cache e ects. We introduce a modi cation of the QRP algorithm which allows the use of BLAS Level 3 kernels while maintaining the numerical behavior of the LINPACK and LAPACK implementations. Experimental comparisons of this approach with the LINPACK and LAPACK implementations on IBM RS/6000, SGI R8000, and DEC Alpha platforms show considerable performance improvements.
منابع مشابه
Parallelization of the QR Decomposition with Column Pivoting Using Column Cyclic Distribution on Multicore and GPU Processors
The QR decomposition with column pivoting (QRP) of a matrix is widely used for rank revealing. The performance of LAPACK implementation (DGEQP3) of the Householder QRP algorithm is limited by Level 2 BLAS operations required for updating the column norms. In this paper, we propose an implementation of the QRP algorithm using a distribution of the matrix columns in a round-robin fashion for bett...
متن کاملMultifrontal multithreaded rank-revealing sparse QR factorization
SuiteSparseQR is a sparse QR factorization package based on the multifrontal method. Within each frontal matrix, LAPACK and the multithreaded BLAS enable the method to obtain high performance on multicore architectures. Parallelism across different frontal matrices is handled with Intel’s Threading Building Blocks library. The symbolic analysis and ordering phase preeliminates singletons by per...
متن کاملLU factorization with panel rank revealing pivoting and its communication avoiding version
We present the LU decomposition with panel rank revealing pivoting (LU PRRP), an LU factorization algorithm based on strong rank revealing QR panel factorization. LU PRRP is more stable than Gaussian elimination with partial pivoting (GEPP), with a theoretical upper bound of the growth factor of (1+ τb) n b , where b is the size of the panel used during the block factorization, τ is a parameter...
متن کاملBlocked and Recursive Algorithms for Triangular Tridiagonalization
We present partitioned (blocked) algorithms for reducing a symmetric matrix to a tridiagonal form, with partial pivoting. That is, the algorithms compute a factorization PAP = LTL where P is a permutation matrix, L is lower triangular with a unit diagonal, and T is symmetric and tridiagonal. The algorithms are based on the column-by-column methods of Parlett and Reid and of Aasen. Our implement...
متن کاملHouseholder QR Factorization With Randomization for Column Pivoting (HQRRP)
A fundamental problem when adding column pivoting to the Householder QR factorization is that only about half of the computation can be cast in terms of high performing matrixmatrix multiplications, which greatly limits the benefits that can be derived from so-called blocking of algorithms. This paper describes a technique for selecting groups of pivot vectors by means of randomized projections...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Scientific Computing
دوره 19 شماره
صفحات -
تاریخ انتشار 1998