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)
The growth factor and efficiency of Gaussian elimination with rook pivoting
Journal of Computational and Applied Mathematics - Special issue: dedicated to William B. Gragg on the occasion of his 60th Birthday
Accurate Symmetric Indefinite Linear Equation Solvers
SIAM Journal on Matrix Analysis and Applications
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Making sparse Gaussian elimination scalable by static pivoting
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
SIAM Journal on Matrix Analysis and Applications
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
MA57---a code for the solution of sparse symmetric definite and indefinite systems
ACM Transactions on Mathematical Software (TOMS)
A fully portable high performance minimal storage hybrid format Cholesky algorithm
ACM Transactions on Mathematical Software (TOMS)
A Note on GMRES Preconditioned by a Perturbed $L D L^T$ Decomposition with Static Pivoting
SIAM Journal on Scientific Computing
SIAM Journal on Matrix Analysis and Applications
An out-of-core sparse Cholesky solver
ACM Transactions on Mathematical Software (TOMS)
The libflame Library for Dense Matrix Computations
IEEE Design & Test
Scaling and pivoting in an out-of-core sparse direct solver
ACM Transactions on Mathematical Software (TOMS)
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Pivoting strategies for tough sparse indefinite systems
ACM Transactions on Mathematical Software (TOMS)
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At the heart of a frontal or multifrontal solver for the solution of sparse symmetric sets of linear equations, there is the need to partially factorize dense matrices (the frontal matrices) and to be able to use their factorizations in subsequent forward and backward substitutions. For a large problem, packing (holding only the lower or upper triangular part) is important to save memory. It has long been recognized that blocking is the key to efficiency and this has become particularly relevant on modern hardware. For stability in the indefinite case, the use of interchanges and 2 × 2 pivots as well as 1 × 1 pivots is equally well established. In this article, the challenge of using these three ideas (packing, blocking, and pivoting) together is addressed to achieve stable factorizations of large real-world symmetric indefinite problems with good execution speed. The ideas are not restricted to frontal and multifrontal solvers and are applicable whenever partial or complete factorizations of dense symmetric indefinite matrices are needed.