Large sparse numerical optimization
Large sparse numerical optimization
Parallel algorithms on the CEDAR system
Proc. of the conference on algorithms and hardware for parallel processing on CONPAR 86
The WY representation for products of householder matrices
SIAM Journal on Scientific and Statistical Computing - Papers from the Second Conference on Parallel Processing for Scientific Computin
An extended set of FORTRAN basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
Incremental condition estimation
SIAM Journal on Matrix Analysis and Applications
A linear algebra library for high-performance computers
Parallel supercomputing: methods, algorithms and applications
A parallel QR factorization algorithm with controlled local pivoting
SIAM Journal on Scientific and Statistical Computing
A Pipelined Block QR Decomposition Algorithm
Proceedings of the Third SIAM Conference on Parallel Processing for Scientific Computing
Computing the Singular Value Decomposition on a Distributed System of Vector Processors
Computing the Singular Value Decomposition on a Distributed System of Vector Processors
Computing rank-revealing QR factorizations of dense matrices
ACM Transactions on Mathematical Software (TOMS)
An FPGA-based computation model for blocked algorithms
AIC'06 Proceedings of the 6th WSEAS International Conference on Applied Informatics and Communications
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This paper presents a new algorithm for computing the QR factorization of a rank-deficient matrix on high-performance machines. The algorithm is based on the Householder QR factorization algorithm with column pivoting. The traditional pivoting strategy is not well suited for machines with a memory hierarchy since it precludes the use of matrix-matrix operations. However, matrix-matrix operations perform better on those machines than matrix-vector or vector-vector operations since they involve significantly less data movement per floating point operation. We suggest a restricted pivoting strategy which allows us to formulate a block QR factorization algorithm where the bulk of the work is in matrix-matrix operations. Incremental condition estimation is used to ensure the reliability of the restricted pivoting scheme. Implementation results on the Cray 2, Cray X-MP and Cray Y-MP show that the new algorithm performs significantly better than the traditional scheme and can more than halve the cost of computing the QR factorization.