Chein-Shan Liu1, Su-Ying Zhang2, Satya N. Atluri3
CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.1, pp. 29-48, 2012, DOI: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… More >
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