This paper presents an efficient approach to compute the dominant poles for the reduced-order admittance (Y parameter) matrix of lossy interconnects. Using the global approximation technique, the efficient frameworks are constructed to transform the frequency-domain Telegrapher?s equations into compact linear algebraic equations. The dominant poles and residues can be extracted by directly solving the linear equations. The closed-form formulas are derived to compute the low-order dominant poles. Due to high accuracy of the global approximation, the extracted poles can accurately represent the exact admittance matrices in a wide frequency range. By using the recursive convolution technique, the pole-residue models can be represented by companion models, which have linear complexity with respect to the computational time. The presented modeling approaches are shown to preserve passivity. Numerical experiments of transient simulation show that the presented modeling approaches lead to higher efficiency, while maintaining comparable accuracy.