A class of arbitrarily ill conditioned floating-point matrices
SIAM Journal on Matrix Analysis and Applications
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)
Computer Arithmetic in Theory and Practice
Computer Arithmetic in Theory and Practice
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
Convergence of Rump's method for inverting arbitrarily ill-conditioned matrices
Journal of Computational and Applied Mathematics
Accurate Floating-Point Summation Part I: Faithful Rounding
SIAM Journal on Scientific Computing
Accurate Floating-Point Summation Part II: Sign, $K$-Fold Faithful and Rounding to Nearest
SIAM Journal on Scientific Computing
Hi-index | 0.00 |
In this paper, algorithms for accurate matrix factorizations named inverse LU and inverse QR factorizations for extremely ill-conditioned matrices are proposed. The proposed algorithms are based on standard numerical algorithms using pure floating-point arithmetic and accurate dot product. Detailed analysis of the algorithms is presented. As an application of the proposed algorithms, a method of computing accurate solutions of linear systems is also proposed. Numerical results are presented for illustrating the performance of the proposed algorithms. Computing times for the algorithms adaptively change according to the difficulty of given problems.