Matrix computations (3rd ed.)
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.)
Automatically tuned linear algebra software
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
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
High Performance Linear Algebra Package for FORTRAN 90
PARA '98 Proceedings of the 4th International Workshop on Applied Parallel Computing, Large Scale Scientific and Industrial Problems
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
High-Performance Computing in Geomechanics by a Parallel Finite Element Approach
PARA '00 Proceedings of the 5th International Workshop on Applied Parallel Computing, New Paradigms for HPC in Industry and Academia
PARA '02 Proceedings of the 6th International Conference on Applied Parallel Computing Advanced Scientific Computing
Parallelization of Finite Element Package by MPI Library
Proceedings of the 8th European PVM/MPI Users' Group Meeting on Recent Advances in Parallel Virtual Machine and Message Passing Interface
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Recursion leads to automatic variable blocking for dense linear algebra algorithms. The recursion transforms LAPACK level-2 algorithms into level3 codes. For this and other reasons recursion usually speeds up the algorithms. Recursion provides a new, easy and very successful way of programming numerical linear algebra algorithms. Several algorithms for matrix factorization have been implemented and tested. Some of these algorithms are already candidates for the LAPACK library. Recursion has also been successfully applied to the BLAS (Basic Linear Algebra Subprograms). The ATLAS system (Automatically Tuned Linear Algebra Software) uses a recursive coding of the BLAS. The Cholesky factorization algorithm for positive definite matrices, LU factorization for general matrices, and LDLT factorization for symmetric indefinite matrices using recursion are formulated in this paper. Performance graphs of our packed Cholesky and LDLT algorithms are presented here.