Parsimonious Least Norm Approximation
Computational Optimization and Applications
Accurate Solution to Overdetermined Linear Equations with Errors Using L1 Norm Minimization
Computational Optimization and Applications
Journal of Computational and Applied Mathematics
Perceptual audio modeling with exponentially damped sinusoids
Signal Processing - Content-based image and video retrieval
Overview of total least-squares methods
Signal Processing
Subspace methods for multimicrophone speech dereverberation
EURASIP Journal on Applied Signal Processing
Brief paper: Subspace like identification incorporating prior information
Automatica (Journal of IFAC)
Computer algebra software for least squares and total least norm inversion of geophysical models
Computers & Geosciences
High-performance numerical algorithms and software for structured total least squares
Journal of Computational and Applied Mathematics
Structured least squares problems and robust estimators
IEEE Transactions on Signal Processing
Strongly concave star-shaped contour characterization by algebra tools
Signal Processing
Fast deconvolution with approximated PSF by RSTLS with antireflective boundary conditions
Journal of Computational and Applied Mathematics
Short Communication: A rectilinear Gaussian model for estimating straight-line parameters
Journal of Visual Communication and Image Representation
Hi-index | 35.69 |
The total least squares (TLS) method is a generalization of the least squares (LS) method for solving overdetermined sets of linear equations Ax≈b. The TLS method minimizes ||[E|-r]||F, where r=b-(A+E)x, so that (b-r)∈Range (A+E), given A∈Cm×n, with m⩾n and b∈Cm×1. The most common TLS algorithm is based on the singular value decomposition (SVD) of [A/b]. However, the SVD-based methods may not be appropriate when the matrix A has a special structure since they do not preserve the structure. Previously, a new problem formulation known as structured total least norm (STLN), and the algorithm for computing the STLN solution, have been developed. The STLN method preserves the special structure of A or [A/b] and can minimize the error in the discrete Lp norm, where p=1, 2 or ∞. In this paper, the STLN problem formulation is generalized for computing the solution of STLN problems with multiple right-hand sides AX≈B. It is shown that these problems can be converted to ordinary STLN problems with one right-hand side. In addition, the method is shown to converge to the optimal solution in certain model reduction problems. Furthermore, the application of the STLN method to various parameter estimation problems is studied in which the computed correction matrix applied to A or [A/B] keeps the same Toeplitz structure as the data matrix A of [A/B], respectively. In particular, the L2 norm STLN method is compared with the LS and TLS methods in deconvolution, transfer function modeling, and linear prediction problems