An extended set of FORTRAN basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
Exploiting functional parallelism of POWER2 to design high-performance numerical algorithms
IBM Journal of Research and Development
ACM Transactions on Mathematical Software (TOMS)
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
Recursion leads to automatic variable blocking for dense linear-algebra algorithms
IBM Journal of Research and Development
Nonlinear array layouts for hierarchical memory systems
ICS '99 Proceedings of the 13th international conference on Supercomputing
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Basic Linear Algebra Subprograms for Fortran Usage
ACM Transactions on Mathematical Software (TOMS)
A recursive formulation of Cholesky factorization of a matrix in packed storage
ACM Transactions on Mathematical Software (TOMS)
Recursive Formulation of Cholesky Algorithm in Fortran 90
PARA '98 Proceedings of the 4th International Workshop on Applied Parallel Computing, Large Scale Scientific and Industrial Problems
PARA '02 Proceedings of the 6th International Conference on Applied Parallel Computing Advanced Scientific Computing
Minimal-storage high-performance Cholesky factorization via blocking and recursion
IBM Journal of Research and Development
Algorithm 865: Fortran 95 subroutines for Cholesky factorization in block hybrid format
ACM Transactions on Mathematical Software (TOMS)
An out-of-core sparse Cholesky solver
ACM Transactions on Mathematical Software (TOMS)
Rectangular full packed format for cholesky's algorithm: factorization, solution, and inversion
ACM Transactions on Mathematical Software (TOMS)
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
Rectangular full packed format for LAPACK algorithms timings on several computers
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
The design of a new out-of-core multifrontal solver
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
New data structures for matrices and specialized inner kernels: low overhead for high performance
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
Partial factorization of a dense symmetric indefinite matrix
ACM Transactions on Mathematical Software (TOMS)
Design of a Multicore Sparse Cholesky Factorization Using DAGs
SIAM Journal on Scientific Computing
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
High performance linear algebra algorithms: an introduction
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume Part I
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
Cache blocking for linear algebra algorithms
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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We consider the efficient implementation of the Cholesky solution of symmetric positive-definite dense linear systems of equations using packed storage. We take the same starting point as that of LINPACK and LAPACK, with the upper (or lower) triangular part of the matrix stored by columns. Following LINPACK and LAPACK, we overwrite the given matrix by its Cholesky factor. We consider the use of a hybrid format in which blocks of the matrices are held contiguously and compare this to the present LAPACK code. Code based on this format has the storage advantages of the present code but substantially outperforms it. Furthermore, it compares favorably to using conventional full format (LAPACK) and using the recursive format of Andersen et al. [2001].