Matrix computations (3rd ed.)
On accurate floating-point summation
Communications of the ACM
Design, implementation and testing of extended and mixed precision BLAS
ACM Transactions on Mathematical Software (TOMS)
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Accurate and Efficient Floating Point Summation
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Accurate Floating-Point Summation Part I: Faithful Rounding
SIAM Journal on Scientific Computing
Fast enclosure for solutions in underdetermined systems
Journal of Computational and Applied Mathematics
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
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New algorithms are presented for computing verified error bounds for least squares problems and underdetermined linear systems. In contrast to previous approaches the new methods do not rely on normal equations and are applicable to sparse matrices. Computational results demonstrate that the new methods are faster than existing ones.