A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
The cache performance and optimizations of blocked algorithms
ASPLOS IV Proceedings of the fourth international conference on Architectural support for programming languages and operating systems
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
MOB forms: a class of multilevel block algorithms for dense linear algebra operations
ICS '94 Proceedings of the 8th international conference on Supercomputing
Exploiting functional parallelism of POWER2 to design high-performance numerical algorithms
IBM Journal of Research and Development
Data prefetching and multilevel blocking for linear algebra operations
ICS '96 Proceedings of the 10th international conference on Supercomputing
Auto-blocking matrix-multiplication or tracking BLAS3 performance from source code
PPOPP '97 Proceedings of the sixth ACM SIGPLAN symposium on Principles and practice of parallel programming
Locality of Reference in LU Decomposition with Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
Recursion leads to automatic variable blocking for dense linear-algebra algorithms
IBM Journal of Research and Development
GEMM-based level 3 BLAS: high-performance model implementations and performance evaluation benchmark
ACM Transactions on Mathematical Software (TOMS)
Nonlinear array layouts for hierarchical memory systems
ICS '99 Proceedings of the 13th international conference on Supercomputing
Organizing matrices and matrix operations for paged memory systems
Communications of the ACM
A recursive formulation of Cholesky factorization of a matrix in packed storage
ACM Transactions on Mathematical Software (TOMS)
Automatically tuned linear algebra software
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
A Family of High-Performance Matrix Multiplication Algorithms
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Recursive Blocked Data Formats and BLAS's for Dense Linear Algebra Algorithms
PARA '98 Proceedings of the 4th International Workshop on Applied Parallel Computing, Large Scale Scientific and Industrial Problems
ECOOP '98 Workshop ion on Object-Oriented Technology
New Generalized Matrix Data Structures Lead to a Variety of High-Performance Algorithms
Proceedings of the IFIP TC2/WG2.5 Working Conference on the Architecture of Scientific Software
Tiling, Block Data Layout, and Memory Hierarchy Performance
IEEE Transactions on Parallel and Distributed Systems
High-performance linear algebra algorithms using new generalized data structures for matrices
IBM Journal of Research and Development
A fully portable high performance minimal storage hybrid format Cholesky algorithm
ACM Transactions on Mathematical Software (TOMS)
Anatomy of high-performance matrix multiplication
ACM Transactions on Mathematical Software (TOMS)
High-performance implementation of the level-3 BLAS
ACM Transactions on Mathematical Software (TOMS)
Design and exploitation of a high-performance SIMD floating-point unit for Blue Gene/L
IBM Journal of Research and Development
Cache oblivious matrix operations using Peano curves
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Minimal data copy for dense linear algebra factorization
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Using non-canonical array layouts in dense matrix operations
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Is cache-oblivious DGEMM viable?
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Compiler-optimized kernels: an efficient alternative to hand-coded inner kernels
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part V
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
A new array format for symmetric and triangular matrices
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
New level-3 BLAS kernels for cholesky factorization
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
Level-3 Cholesky Factorization Routines Improve Performance of Many Cholesky Algorithms
ACM Transactions on Mathematical Software (TOMS)
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Dense linear algebra codes are often expressed and coded in terms of BLAS calls. This approach, however, achieves suboptimal performance due to the overheads associated to such calls. Taking as an example the dense Cholesky factorization of a symmetric positive definite matrix we show that the potential of non-canonical data structures for dense linear algebra can be better exploited with the use of specialized inner kernels. The use of non-canonical data structures together with specialized inner kernels has low overhead and can produce excellent performance.