Open Access

ARTICLE

The Jordan Structure of Residual Dynamics Used to Solve Linear Inverse Problems

Chein-Shan Liu¹, Su-Ying Zhang², Satya N. Atluri³

1 Department of Civil Engineering, National Taiwan University, Taipei, Taiwan. E-mail: liucs@ntu.edu.tw
2 College of Physics and Electronic Engineering, Shanxi University, Taiyuan, China.
3 Center for Aerospace Research & Education, University of California, Irvine

Computer Modeling in Engineering & Sciences 2012, 88(1), 29-48. https://doi.org/10.3970/cmes.2012.088.029

Abstract

With a detailed investigation of n linear algebraic equations Bx=b, we find that the scaled residual dynamics for y∈Sⁿ⁻¹ is equipped with four structures: the Jordan dynamics, the rotation group SO(n), a generalized Hamiltonian formulation, as well as a metric bracket system. Therefore, it is the first time that we can compute the steplength used in the iterative method by a novel algorithm based on the Jordan structure. The algorithms preserving the length of y are developed as the structure preserving algorithms (SPAs), which can significantly accelerate the convergence speed and are robust enough against the noise in the numerical solutions of ill-posed linear inverse problems.

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Keywords

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