## Abstract

With a detailed investigation of n linear algebraic equations Bx = b, we find that the scaled residual dynamics for y ∈ S^{n-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.

Original language | English |
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Pages (from-to) | 29-47 |

Number of pages | 19 |

Journal | CMES - Computer Modeling in Engineering and Sciences |

Volume | 88 |

Issue number | 1 |

State | Published - 2012 |

## Keywords

- Future cone
- Generalized Hamiltonian formulation
- Ill-posed linear system
- Jordan dynamics
- Linear inverse problems
- Metric bracket system
- Structure preserving algorithms (SPAs)