@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: <b>Bx = b</b>. We define a future cone in the Minkowski space as an invariant manifold, wherein the discrete dynamics evolves. A critical value α<sub>c</sub>  in the critical descent vector <b>u = α<sub>c</sub>r + B<sup>T</sup>r</b> is derived, which renders the largest convergence rate as to be the <b>globally optimal iterative algorithm</b> (GOIA) among all the numerically iterative algorithms with the descent vector having the form <b>u = αr + B<sup>T</sup>r</b> 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}
}