This paper describes the details of the iteration process used to determine the transfer functions of linear time-invariant (LTI) circuits causing the memory effect of power amplifier (PA). An outline of the method is reported in our work presented at ICCS2012. The accuracy of the method is improved by using cross-correlation spectra at three signal levels, and its validity is confirmed by a computer simulation. The method can be applied to online updating of PAs operating in mobile communication systems. The updating is realized separately from the fast varying nonlinear coefficients. The possibility of updating with a short interval is indirectly shown for the nonlinear coefficients using a procedure similar to that of memoryless PAs. For PAs characterized by the method, this paper also describes the inverses that cancel the nonlinear distortion with minimum complexity. The validity of the inverse is confirmed by a computer simulation on the power spectrum of the PA for orthogonal frequency-division multiplexing (OFDM) signals with 500 subcarriers. The simulated spectra show that the fifth order or higher inverses are effective in keeping adjacent channel leakage power ratio (ACLR) lower than -60 dB at the practical signal level. Improvements in the error vector magnitude (EVM) due to the inverse were also confirmed by reductions of gain and phase variations under varying envelope conditions.