TY - EJOU
AU - Liu, Chein-Shan
TI - A Globally Optimal Iterative Algorithm to Solve an Ill-Posed Linear System
T2 - Computer Modeling in Engineering \& Sciences
PY - 2012
VL - 84
IS - 4
SN - 1526-1506
AB - 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.
KW - Ill-posed linear system
KW - Globally optimal iterative algorithm (GOIA)
KW - Future cone
KW - Invariant-manifold
DO - 10.3970/cmes.2012.084.383