Large-scale algebraic Riccati equations with high-rank constant terms

Bo Yu, Hung Yuan Fan*, Eric King wah Chu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


We consider the numerical solution of large-scale algebraic Riccati equations with high-rank constant terms. The solutions are not numerically low-rank, so the previously successful methods based on low-rank representations are not directly applicable. We modify the doubling algorithm, making use of the low-rank in the input matrix B. We also solve the challenging problems in the estimation of residuals and relative errors, convergence control and the output of the modified algorithm. Illustrative numerical examples are presented.

Original languageEnglish
Pages (from-to)130-143
Number of pages14
JournalJournal of Computational and Applied Mathematics
Publication statusPublished - 2019 Dec 1


  • Algebraic Riccati equation
  • Feedback gain
  • High-rank constant term
  • LQR optimal control
  • Large-scale problem

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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