The total least squares (TLS) method is a well-known technique for solving an overdetermined linear system of equations Ax ≈ b, that is appropriate when both the coefficient matrix A and the right-hand side vector b are contaminated by some noise. For ill-posed TLS poblems, regularization techniques are necessary to stabilize the computed solution; otherwise, TLS produces a noise-dominant output. In this paper, we show that the regularized total least squares (RTLS) problem can be reformulated as a nonlinear least squares problem and can be solved by the Gauss–Newton method. Due to the nature of the RTLS problem, we present an appropriate method to choose a good regularization parameter and also a good initial guess. Finally, the efficiency of the proposed method is examined by some test problems.

总最小二乘法 (TLS) 是一种众所周知的技术，用于求解方程A x ≈ b的超定线性系统，适用于系数矩阵A和右侧向量b被一些噪音污染了。对于不适定的 TLS 问题，需要正则化技术来稳定计算的解决方案；否则，TLS 会产生以噪声为主的输出。在本文中，我们表明正则化总最小二乘 (RTLS) 问题可以重新表述为非线性最小二乘问题，并且可以通过高斯-牛顿方法解决。由于 RTLS 问题的性质，我们提出了一种合适的方法来选择一个好的正则化参数和一个好的初始猜测。最后，通过一些测试问题来检验所提出方法的有效性。