Solving algebraic problems with high accuracy
Proc. of the symposium on A new approach to scientific computation
Improved error bounds for underdetermined system solvers
SIAM Journal on Matrix Analysis and Applications
Optimal Backward Perturbation Bounds for Underdetermined Systems
SIAM Journal on Matrix Analysis and Applications
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
A method of obtaining verified solutions for linear systems suited for Java
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Improved solution enclosures for over- and underdetermined interval linear systems
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Verified Bounds for Least Squares Problems and Underdetermined Linear Systems
SIAM Journal on Matrix Analysis and Applications
| Hi-index | 7.29 |
Fast algorithms for enclosing minimal 2-norm solutions in underdetermined systems are proposed. For developing these algorithms, theory for computing error bounds for numerical solutions is established. Moreover techniques for accelerating the enclosure and obtaining smaller error bounds are introduced. Numerical results show the properties of the proposed algorithms.