An extended set of FORTRAN basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
MIPS RISC architecture
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
The SPARC architecture manual: version 8
The SPARC architecture manual: version 8
Alpha architecture reference manual
Alpha architecture reference manual
LAPACK's user's guide
ACM Transactions on Mathematical Software (TOMS)
Matrix computations (3rd ed.)
Basic Linear Algebra Subprograms for Fortran Usage
ACM Transactions on Mathematical Software (TOMS)
Accurate eigenvalues of a symmetric tri-diagonal matrix
Accurate eigenvalues of a symmetric tri-diagonal matrix
LAPACK Working Note No. 36: Robust Triangular Solves for Use in Condition Estimation
LAPACK Working Note No. 36: Robust Triangular Solves for Use in Condition Estimation
Handling floating-point exceptions in numeric programs
ACM Transactions on Programming Languages and Systems (TOPLAS)
Technical report for floating-point exception handling
ACM SIGPLAN Fortran Forum - Special issue: draft technical reports
Design, implementation and testing of extended and mixed precision BLAS
ACM Transactions on Mathematical Software (TOMS)
On computing givens rotations reliably and efficiently
ACM Transactions on Mathematical Software (TOMS)
The design and implementation of the MRRR algorithm
ACM Transactions on Mathematical Software (TOMS)
Reliable Eigenvalues of Symmetric Tridiagonals
SIAM Journal on Matrix Analysis and Applications
| Hi-index | 14.98 |
An attractive paradigm for building fast numerical algorithms is the following: 1) try a fast but occasionally unstable algorithm, 2) test the accuracy of the computed answer, and 3) recompute the answer slowly and accurately in the unlikely event it is necessary. This is especially attractive on parallel machines where the fastest algorithms may be less stable than the best serial algorithms. Since unstable algorithms can overflow or cause other exceptions, exception handling is needed to implement this paradigm safely. To implement it efficiently, exception handling cannot be too slow. We illustrate this paradigm with numerical linear algebra algorithms from the LAPACK library.