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

Chein-Shan Liu1
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 αc in the critical descent vector u = αcr + BTr 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 + BTr to solve the ill-posed linear problems. Some numerical examples are used to reveal the superior performance of the GOIA.

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Cite This Article

Liu, C. (2012). A Globally Optimal Iterative Algorithm to Solve an Ill-Posed Linear System. CMES-Computer Modeling in Engineering & Sciences, 84(4), 383–404.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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