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
Optimizing matrix multiply using PHiPAC: a portable, high-performance, ANSI C coding methodology
ICS '97 Proceedings of the 11th international conference on Supercomputing
Applied numerical linear algebra
Applied numerical linear algebra
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)
Fortran 90/95 explained (2nd ed.)
Fortran 90/95 explained (2nd ed.)
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)
LAPACK95 users' guide
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
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 '98 Proceedings of the 4th International Workshop on Applied Parallel Computing, Large Scale Scientific and Industrial Problems
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
LAWRA: Linear Algebra with Recursive Algorithms
PARA '00 Proceedings of the 5th International Workshop on Applied Parallel Computing, New Paradigms for HPC in Industry and Academia
A Fast Minimal Storage Symmetric Indefinite Solver
PARA '00 Proceedings of the 5th International Workshop on Applied Parallel Computing, New Paradigms for HPC in Industry and Academia
Experience with a Recursive Perturbation Based Algorithm for Symmetric Indefinite Linear Systems
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Applying recursion to serial and parallel QR factorization leads to better performance
IBM Journal of Research and Development
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)
Families of algorithms related to the inversion of a Symmetric Positive Definite matrix
ACM Transactions on Mathematical Software (TOMS)
Rectangular full packed format for cholesky's algorithm: factorization, solution, and inversion
ACM Transactions on Mathematical Software (TOMS)
Algorithms for memory hierarchies: advanced lectures
Algorithms for memory hierarchies: advanced lectures
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
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A new Recursive Packed Inverse Calculation Algorithm for symmetric positive definite matrices has been developed. The new Recursive Inverse Calculation algorithm uses minimal storage, n(n + 1)/2, and has nearly the same performance as the LAPACK full storage algorithm using n2 memory words. New recursive packed BLAS needed for this algorithm have been developed too. Two transformation routines, from the LAPACK packed storage data format to the recursive storage data format were added to the package too.We present performance measurements on several current architectures that demonstrate improvements over the traditional packed routines.