Stable Dynamic Mode Decomposition Algorithm for Noisy Pressure-Sensitive Paint Measurement Data

The paper defines T‑TLS DMD by forming the reduced augmented matrix, taking its SVD, partitioning V, and setting the reduced operator to A~ = V21 V11^+, with k chosen to minimize E(k) = ||Y − A~ X~||^2; it notes that k=r recovers classical TLS DMD and documents, via experiments, that standard/exact DMD exhibit inward (damping) bias while T‑TLS improves stability/variance relative to TLS DMD . The candidate solution reconstructs these facts algebraically (A~ = V21 V11^+, equivalence at k=r), shows the DMD eigenpair lifting φ_DMD = P_r φ, proves existence of an optimal k, explains standard/exact DMD attenuation bias through an errors‑in‑variables argument, and provides a perturbation-based rationale (Wedin + Bauer–Fike) for why truncation reduces variance. The paper’s argument is primarily empirical while the model provides a proof-oriented sketch; they agree on substance and differ mainly in the style of justification.