The Jordan structure of residual dynamics used to solve linear inverse problems

Chein Shan Liu, Su Ying Zhang, Satya N. Atluri

Research output: Contribution to journalArticle

2 Scopus citations

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.

Original languageEnglish
Pages (from-to)29-47
Number of pages19
JournalCMES - Computer Modeling in Engineering and Sciences
Volume88
Issue number1
StatePublished - 2012

Keywords

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

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