Open Access

ARTICLE

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

Chein-Shan Liu¹

1 Department of Civil Engineering, National Taiwan University, Taipei, Taiwan. E-mail: liucs@ntu.edu.tw

Computer Modeling in Engineering & Sciences 2012, 84(4), 383-404. https://doi.org/10.3970/cmes.2012.084.383

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_cr + B^Tr 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^Tr to solve the ill-posed linear problems. Some numerical examples are used to reveal the superior performance of the GOIA.

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Keywords

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