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<p>In this paper, within a separable Hilbert space, a mathematical representation for solving the total least squares (TLS) problem is derived through the application of singular value decomposition techniques applied on finite-rank operators. Additionally, a numerical example is presented to calculate the solution of this problem. Furthermore, based on the properties of eigenvalues of block operators, an existence condition for stable solutions of the regularized TLS problem is derived.</p>

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Solution of total least squares problem in Hilbert spaces

  • 期刊论文

  • 发表日期：

    2025年12月16日

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  • Yuhang Liu,
  • Haifeng Ma

摘要

In this paper, within a separable Hilbert space, a mathematical representation for solving the total least squares (TLS) problem is derived through the application of singular value decomposition techniques applied on finite-rank operators. Additionally, a numerical example is presented to calculate the solution of this problem. Furthermore, based on the properties of eigenvalues of block operators, an existence condition for stable solutions of the regularized TLS problem is derived.