Another look at Residual Dynamic Mode Decomposition in the regime of fewer Snapshots than Dictionary Size

Matthew J. Colbrook

correctmedium confidence

Category: math.DS
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The candidate solution reproduces the paper’s residual formulations for exact DMD and kernelized EDMD via the same dual least-squares viewpoint and derives the same pseudospectral minimization principle. It also correctly notes complex-conjugation in cross terms for complex scalars, clarifying minor typographical slips in the paper (e.g., missing conjugates and the statement K̂* v = λ̄ v for a left eigenvector). Substantively, both arrive at the same formulas and algorithmic consequences.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The manuscript provides a cohesive dual least-squares perspective for ResDMD in data-limited regimes that unifies exact DMD and kernelized EDMD, enabling residual-based validation and pseudospectral computations using reduced matrices. The derivations are technically sound and the algorithms are practical. Minor notational issues (complex conjugation in cross terms; adjoint relation for left eigenvectors) should be corrected to prevent confusion. With these fixes, the paper is a solid and useful contribution to data-driven Koopman analysis.