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
Implementation of the GMRES method using householder transformations
SIAM Journal on Scientific and Statistical Computing - Telecommunication Programs at U.S. Universities
A storage-efficient WY representation for products of householder transformations
SIAM Journal on Scientific and Statistical Computing
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
Modification of the householder method based on the compact WY representation
SIAM Journal on Scientific and Statistical Computing
On Hyperbolic Triangularization: Stability and Pivoting
SIAM Journal on Matrix Analysis and Applications
Aggregations of Elementary Transformations
Aggregations of Elementary Transformations
Parallel out-of-core computation and updating of the QR factorization
ACM Transactions on Mathematical Software (TOMS)
Accumulating Householder transformations, revisited
ACM Transactions on Mathematical Software (TOMS)
Supermatrix out-of-order scheduling of matrix operations for SMP and multi-core architectures
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Scheduling of QR Factorization Algorithms on SMP and Multi-Core Architectures
PDP '08 Proceedings of the 16th Euromicro Conference on Parallel, Distributed and Network-Based Processing (PDP 2008)
Updating an LU Factorization with Pivoting
ACM Transactions on Mathematical Software (TOMS)
Parallel tiled QR factorization for multicore architectures
Concurrency and Computation: Practice & Experience
Programming matrix algorithms-by-blocks for thread-level parallelism
ACM Transactions on Mathematical Software (TOMS)
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We present high-performance algorithms for up-and-downdating a Cholesky factor or QR factorization. The method uses Householder-like transformations, sometimes called hyperbolic Householder transformations, that are accumulated so that most computation can be cast in terms of high-performance matrix-matrix operations. The resulting algorithms can then be used as building blocks for an algorithm-by-blocks that allows computation to be conveniently scheduled to multithreaded architectures like multicore processors. Performance is shown to be similar to that achieved by a blocked QR factorization via Householder transformations.