In the existing algorithm for fault diagnosis in analog circuits, artificial intelligence-based fault diagnosis algorithms require a large amount of training data and long training time, making it difficult to achieve parameter identification. Traditional circuit analysis methods require multiple test points and involve complex calculations. Based on this, a fault diagnosis algorithm for analog circuits based on optimized matrix perturbation analysis is proposed. Firstly, the Laplace operator is used to convolve the output response matrix of the tested circuit, thereby enhancing the perturbation pattern between matrix elements and circuit component parameters. Secondly, the trace and spectral radius of the matrix are selected as fault characteristics, and a matrix model is established using this perturbation pattern. Then, an improved diagnostic algorithm is used to verify examples in Sallen_Key bandpass filter circuits and leapfrog low-pass filter circuits. The results show that with only one test point, the proposed method can achieve parameter identification of faulty components. The fault diagnosis rate reaches 100%, with parameter identification error controlled within 1%, and computation time controlled at millisecond level. Therefore, this method is easy to implement for online testing and suitable for situations requiring high accuracy in fault localization and precise parameter identification.