Total least squares (TLS) methods have been widely used in data fitting. Compared with the least squares method, for TLS problem we takes into account not only the observation errors, but also the errors in the measurement matrix. This is more realistic in practical applications. For the large-scale discrete ill-posed problem $Ax \approx b$, we introduce the quantum-inspired techniques to approximate the truncated total least squares (TTLS) solution. We analyze the accuracy of the quantum-inspired truncated total least squares algorithm and perform numerical experiments to demonstrate the efficiency of our method.
翻译:总最小方块( TLS) 方法在数据安装中被广泛使用。 与最小方块方法相比, 我们不仅考虑到观察错误, 也考虑到测量矩阵中的错误。 这在实际应用中更为现实。 对于大型离散不测问题 $Ax\ approx b$, 我们引入量子激发技术, 以接近短小总最小方块( TTLS) 解决方案。 我们分析量子激发的快速总最小方块算法的准确性, 并进行数字实验以证明我们方法的效率 。