Abstract
We examine the behavior of Newton's method in floating point arithmetic, allowing for extended precision in computation of the residual, inaccurate evaluation of the Jacobian and unstable solution of the linear systems. We bound the limiting accuracy and the smallest norm of the residual. The application that motivates this work is iterative refinement for the generalized eigenvalue problem. We show that iterative refinement by Newton's method can be used to improve the forward and backward errors of computed eigenpairs.
| Original language | English |
|---|---|
| Pages (from-to) | 1038-1057 |
| Number of pages | 19 |
| Journal | SIAM Journal on Matrix Analysis and Applications |
| Volume | 22 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Jan 2001 |
Keywords
- Backward error
- Cholesky method
- Forward error
- Generalized eigenvalue problem
- Iterative refinement
- Limiting accuracy
- Limiting residual
- Newton's method
- Rounding error analysis