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Modified Quasi-Newton Methods for Solving Systems of Linear Equations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Shi, Yixun |
| Copyright Year | 2007 |
| Abstract | Quasi-Newton methods for unconstrained optimization problems are considered for solving a system of linear equations Ax = b where A ∈ R n×n , Rank(A )= n, b ∈ R n , and x ∈ R n is the vector of unknowns. This problem can be converted into an equivalent quadratic optimization problem. Based on the observation that if H ≈ (A T A) −1 = A −1 (A T ) −1 then ¯ x = HA T b can be taken as an approximate solution of the problem, we propose a modification to the Quasi-Newton method. The modified algorithm incorporates the above observation. Global convergence is ensured by adding the steepest descent direction into the combination. Numerical experiments are also reported. |
| Starting Page | 737 |
| Ending Page | 744 |
| Page Count | 8 |
| File Format | PDF HTM / HTML |
| DOI | 10.12988/ijcms.2007.07072 |
| Volume Number | 2 |
| Alternate Webpage(s) | http://www.m-hikari.com/ijcms-password2007/13-16-2007/shiIJCMS13-16-2007.pdf |
| Alternate Webpage(s) | https://doi.org/10.12988/ijcms.2007.07072 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
