A Globally Optimal Iterative Algorithm to Solve an Ill-Posed Linear System

作者：Liu Chein Shan^*

来源：Computer Modeling in Engineering & Sciences, 2012, 84(4): 383-403.

• Ill-posed linear system
• Globally optimal iterative algorithm (GOIA)
• Future cone
• Invariant-manifold

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 alpha(c) in the critical descent vector u = alpha(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 = alpha r + B(T)r to solve the ill-posed linear problems. Some numerical examples are used to reveal the superior performance of the GOIA.

• 出版日期2012-4