2101.04566
Frequency Limited H2 Optimal Model Reduction of Large-Scale Sparse Dynamical Systems
Xin Du, M. Monir Uddin, A. Mostakim Fony, Md. Tanzim Hossain, Mohammaed Sahadat-Hossain
incompletemedium confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper correctly sets up the frequency-limited Gramians via matrix logarithms and derives the frequency-limited Sylvester equations used in TSIA, and for index-1 descriptors it explicitly proves that the dense Schur-complement solve is equivalent to a sparse augmented block solve. However, it only asserts (without proof) that the resulting TSIA fixed points satisfy frequency-limited Wilson first-order optimality conditions. The candidate solution supplies the missing hypotheses (stability, disjoint spectra, existence of principal logs) and a cogent Lagrangian/Fréchet-derivative proof sketch showing that TSIA fixed points solve the Wilson conditions for the ω-limited H2 objective, and reproduces the index-1 block-equivalence argument.
Referee report (LaTeX)
\textbf{Recommendation:} major revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The manuscript contributes practical techniques for frequency-limited H2 model reduction and a solid sparsity-preserving treatment for index-1 descriptor systems. However, it lacks a rigorous derivation of the frequency-limited first-order optimality (Wilson) conditions that it claims. The theoretical argument should be completed by deriving the gradients of the frequency-limited cost under clear assumptions. Resolving a minor inconsistency in the projection formula for B-hat and explicitly stating the spectral/logarithm assumptions will significantly improve correctness and clarity.