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Jaehong Oh

∑Notes

Theorem F — Spectral Stability

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  1. #1

    Denominator perturbation: .

    ∣ϕ′−ϕ∣=∣cut+Δcvol+Δv−cutvol∣=∣Δc⋅vol−cut⋅Δv(vol+Δv)⋅vol∣.|\phi'-\phi|=\left|\frac{\mathrm{cut}+\Delta_c}{\mathrm{vol}+\Delta_v}-\frac{\mathrm{cut}}{\mathrm{vol}}\right|=\left|\frac{\Delta_c\cdot\mathrm{vol}-\mathrm{cut}\cdot\Delta_v}{(\mathrm{vol}+\Delta_v)\cdot\mathrm{vol}}\right|.