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)
ACM Transactions on Mathematical Software (TOMS)
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
Locality of Reference in LU Decomposition with Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
Improving the memory-system performance of sparse-matrix vector multiplication
IBM Journal of Research and Development
Recursion leads to automatic variable blocking for dense linear-algebra algorithms
IBM Journal of Research and Development
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Basic Linear Algebra Subprograms for Fortran Usage
ACM Transactions on Mathematical Software (TOMS)
A Storage Efficient WY Representation for Products of Householder Transformations
A Storage Efficient WY Representation for Products of Householder Transformations
Parallel out-of-core computation and updating of the QR factorization
ACM Transactions on Mathematical Software (TOMS)
Minimizing development and maintenance costs in supporting persistently optimized BLAS
Software—Practice & Experience - Research Articles
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
Scalable parallelization of FLAME code via the workqueuing model
ACM Transactions on Mathematical Software (TOMS)
SuperMatrix: a multithreaded runtime scheduling system for algorithms-by-blocks
Proceedings of the 13th ACM SIGPLAN Symposium on Principles and practice of parallel programming
Anatomy of high-performance matrix multiplication
ACM Transactions on Mathematical Software (TOMS)
Parallel tiled QR factorization for multicore architectures
Concurrency and Computation: Practice & Experience
Achieving accurate and context-sensitive timing for code optimization
Software—Practice & Experience
Minimizing startup costs for performance-critical threading
IPDPS '09 Proceedings of the 2009 IEEE International Symposium on Parallel&Distributed Processing
Out-of-Core Computation of the QR Factorization on Multi-core Processors
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Dynamic task scheduling for linear algebra algorithms on distributed-memory multicore systems
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
Comparative study of one-sided factorizations with multiple software packages on multi-core hardware
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
Applying recursion to serial and parallel QR factorization leads to better performance
IBM Journal of Research and Development
Scaling LAPACK panel operations using parallel cache assignment
Proceedings of the 15th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming
The impact of multicore on math software
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
In-place transposition of rectangular matrices
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Achieving Scalable Parallelization for the Hessenberg Factorization
CLUSTER '11 Proceedings of the 2011 IEEE International Conference on Cluster Computing
Parallel and Cache-Efficient In-Place Matrix Storage Format Conversion
ACM Transactions on Mathematical Software (TOMS)
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In LAPACK many matrix operations are cast as block algorithms which iteratively process a panel using an unblocked algorithm and then update a remainder matrix using the high performance Level 3 BLAS. The Level 3 BLAS have excellent scaling, but panel processing tends to be bus bound, and thus scales with bus speed rather than the number of processors (p). Amdahl's law therefore ensures that as p grows, the panel computation will become the dominant cost of these LAPACK routines. Our contribution is a novel parallel cache assignment approach to the panel factorization which we show scales well with p. We apply this general approach to the QR, QL, RQ, LQ and LU panel factorizations. We show results for two commodity platforms: an 8-core Intel platform and a 32-core AMD platform. For both platforms and all twenty implementations (five factorizations each of which is available in 4 types), we present results that demonstrate that our approach yields significant speedup over the existing state of the art.