Quantum-inspired algorithm for truncated total least squares solution

Compared with the ordinary least squares method, for total least squares (TLS) problem we take into account not only the observation errors, but also the errors in the measurement matrix, which is more realistic in practical applications. Motivated by recent advances in quantum-inspired computing, which have shown promise for solving a variety of optimization problems. For the large-scale discrete ill-posed problem Ax approximate to b, our proposed method leverages quantum-inspired techniques to perform a truncated singular value decomposition (SVD) of the measurement matrix. This allows us to efficiently approximate the TTLS solution, We analyze the accuracy of the quantum-inspired truncated total least squares algorithm both theoretically and numerically. In our theoretical analysis, we compare the approximation accuracy of the proposed quantum-inspired method with TTLS and RTTLS methods. The results of our numerical experiments demonstrate the efficiency of the proposed method in terms of both approximation accuracy and computational efficiency, and show that it can provide accurate solutions for large-scale ill-posed problems.