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The low-rank approximation associated with the Jacobian is right regarding Broyden's course of quasi-Newton algorithms and Jacobian-free Newton-Krylov practices and offers a complementary formula for the answer of nonlinear systems of equations.Metallic nanogap dimers are extremely useful for enhancing surface-enhanced Raman scattering and differing nonlinear optical effects employing near-field enhancement effects induced because of the localized area plasmon resonance. However, t