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Parallel tiled QR factorization for multicore architectures
, 2007
"... As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these new processors. Fine grain parallelism becomes a major requ ..."
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Cited by 84 (43 self)
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requirement and introduces the necessity of loose synchronization in the parallel execution of an operation. This paper presents an algorithm for the QR factorization where the operations can be represented as a sequence of small tasks that operate on square blocks of data. These tasks can be dynamically
Generalized QR Factorization and its Applications
, 1994
"... The purpose of this note is to reintroduce the generalized QR factorization with or without pivoting of two matrices A and B having the same numberofrows, and whenever B is square and nonsingular, the factorization implicitly gives the orthogonal factorization with or without pivoting of B,1 A. The ..."
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Cited by 2 (0 self)
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The purpose of this note is to reintroduce the generalized QR factorization with or without pivoting of two matrices A and B having the same numberofrows, and whenever B is square and nonsingular, the factorization implicitly gives the orthogonal factorization with or without pivoting of B,1 A
A PARALLEL QRFACTORIZATION/SOLVER OF QUASISEPARABLE MATRICES
"... Abstract. This manuscript focuses on the development of a parallel QRfactorization of structured rank matrices, which can then be used for solving systems of equations. First, we will prove the existence of two types of Givens transformations, named rank decreasing and rank expanding Givens transfo ..."
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Abstract. This manuscript focuses on the development of a parallel QRfactorization of structured rank matrices, which can then be used for solving systems of equations. First, we will prove the existence of two types of Givens transformations, named rank decreasing and rank expanding Givens
LAPACKStyle Codes for the QR Factorization of Banded Matrices ⋆
"... Abstract. In this paper we present unblocked and blocked LAPACKstyle codes for the computation of the QR factorization of a banded matrix. The new routines are evaluated using highlytuned multithreaded implementations of BLAS on two sharedmemory multiprocessors, revealing the performance of the bl ..."
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Abstract. In this paper we present unblocked and blocked LAPACKstyle codes for the computation of the QR factorization of a banded matrix. The new routines are evaluated using highlytuned multithreaded implementations of BLAS on two sharedmemory multiprocessors, revealing the performance
Finding Good Column Orderings for Sparse QR Factorization
 In Second SIAM Conference on Sparse Matrices
, 1996
"... For sparse QR factorization, finding a good column ordering of the matrix to be factorized, is essential. Both the amount of fill in the resulting factors, and the number of floatingpoint operations required by the factorization, are highly dependent on this ordering. A suitable column ordering of ..."
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Cited by 17 (0 self)
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For sparse QR factorization, finding a good column ordering of the matrix to be factorized, is essential. Both the amount of fill in the resulting factors, and the number of floatingpoint operations required by the factorization, are highly dependent on this ordering. A suitable column ordering
QR FACTORIZATIONS USING A RESTRICTED SET OF ROTATIONS
"... Abstract. Any matrix of dimension ( ) can be reduced to upper triangular form by multiplying by a sequence of appropriately chosen rotation matrices. In this work, we address the question of whether such a factorization exists when the set of allowed rotation planes is restricted. We introduce the r ..."
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the rotation graph as a tool to devise elimination orderings in QR factorizations. Properties of this graph characterize sets of rotation planes that are sufficient (or sufficient under permutation) and identify rotation planes to add to complete a deficient set. We also devise a constructive way to determine
Multifrontal multithreaded rankrevealing 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 ..."
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Cited by 16 (2 self)
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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
Sparse Givens QR Factorization on a Multiprocessor
, 1996
"... We present a parallel algorithm for the QR factorization with column pivoting of a sparse matrix by means of Givens rotations. Nonzero elements of the matrix M to be decomposed are stored in a onedimensional doubly linked list data structure. We will discuss a strategy to reduce fillin in order to ..."
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Cited by 3 (3 self)
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We present a parallel algorithm for the QR factorization with column pivoting of a sparse matrix by means of Givens rotations. Nonzero elements of the matrix M to be decomposed are stored in a onedimensional doubly linked list data structure. We will discuss a strategy to reduce fillin in order
HighPerformance Library Software for QR Factorization
 IN APPLIED PARALLEL COMPUTING: NEW PARADIGMS FOR HPC IN INDUSTRY AND ACADEMIA, T. SØRVIK ET AL., EDS., LECTURE NOTES IN COMPUT. SCI. 1947
, 2000
"... In [5, 6], we presented algorithm RGEQR3, a purely recursive formulation of the QR factorization. Using recursion leads us to a natural way to choose the kway aggregating Householder transform of Schreiber and Van Loan [10]. RGEQR3 is a performance critical subroutine for the main (hybrid recur ..."
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Cited by 13 (3 self)
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In [5, 6], we presented algorithm RGEQR3, a purely recursive formulation of the QR factorization. Using recursion leads us to a natural way to choose the kway aggregating Householder transform of Schreiber and Van Loan [10]. RGEQR3 is a performance critical subroutine for the main (hybrid
Results 11  20
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103,016