A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
LAPACK's user's guide
Stability of block algorithms with fast level-3 BLAS
ACM Transactions on Mathematical Software (TOMS)
Matrix computations (3rd ed.)
FLAME: Formal Linear Algebra Methods Environment
ACM Transactions on Mathematical Software (TOMS)
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Solving Linear Systems on Vector and Shared Memory Computers
Solving Linear Systems on Vector and Shared Memory Computers
The science of deriving dense linear algebra algorithms
ACM Transactions on Mathematical Software (TOMS)
Mechanical derivation and systematic analysis of correct linear algebra algorithms
Mechanical derivation and systematic analysis of correct linear algebra algorithms
Knowledge-based automatic generation of partitioned matrix expressions
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
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We introduce a methodology for obtaining inventories of error results for families of numerical dense linear algebra algorithms. The approach for deriving the analyses is goal-oriented, systematic, and layered. The presentation places the analysis side-by-side with the algorithm so that it is obvious where roundoff error is introduced. The approach supports the analysis of more complex algorithms, such as the blocked LU factorization. For this operation we derive a tighter error bound than has been previously reported in the literature.