@Article{cmes.2012.084.383,
AUTHOR = {Chein-Shan Liu},
TITLE = {A Globally Optimal Iterative Algorithm to Solve an Ill-Posed Linear System},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {84},
YEAR = {2012},
NUMBER = {4},
PAGES = {383--404},
URL = {http://www.techscience.com/CMES/v84n4/25821},
ISSN = {1526-1506},
ABSTRACT = {An iterative algorithm based on the critical descent vector is proposed to solve an ill-posed linear system: **Bx = b**. We define a future cone in the Minkowski space as an invariant manifold, wherein the discrete dynamics evolves. A critical value α_{c} in the critical descent vector **u = α**_{c}r + B^{T}r is derived, which renders the largest convergence rate as to be the **globally optimal iterative algorithm** (GOIA) among all the numerically iterative algorithms with the descent vector having the form **u = αr + B**^{T}r to solve the ill-posed linear problems. Some numerical examples are used to reveal the superior performance of the GOIA.},
DOI = {10.3970/cmes.2012.084.383}
}