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A direct rational approximation method based on Thiele interpolating continued fractions theory is proposed for fast frequency sweep analysis of electromagnetic problems. And an adaptive algorithm is also formed. Compared with the conventional rational approximation method, the proposed method can get a rational approximation directly without a great number of matrix inverse computations and doesn't need to allocate much memory for high derivatives of the dense impedance matrix. Meanwhile, the computation of surface currents by continued fractions can be sped up as compared with the traditional rational approximation. Numerical simulations for broad band scattering analysis of different shaped objects are discussed to shown the effectiveness of the present method.