@Article{cmes.2012.088.029,
AUTHOR = {Chein-Shan  Liu, Su-Ying  Zhang, Satya N.  Atluri},
TITLE = {The Jordan Structure of Residual Dynamics Used to Solve Linear Inverse Problems},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {88},
YEAR = {2012},
NUMBER = {1},
PAGES = {29--48},
URL = {http://www.techscience.com/CMES/v88n1/26849},
ISSN = {1526-1506},
ABSTRACT = {With a detailed investigation of n linear algebraic equations <b>Bx=b</b>, we find that the scaled residual dynamics for y∈S<sup>n−1</sup>  is equipped with four structures: the Jordan dynamics, the rotation group <i>SO(n)</i>, 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.},
DOI = {10.3970/cmes.2012.088.029}
}