Parsimonious Least Norm Approximation
Computational Optimization and Applications
Accurate Solution to Overdetermined Linear Equations with Errors Using L1 Norm Minimization
Computational Optimization and Applications
Lower dimensional representation of text data in vector space based information retrieval
Computational information retrieval
Optimal estimation of line segments in noisy lidar data
Signal Processing - Signal processing in UWB communications
Overview of total least-squares methods
Signal Processing
The matrix-restricted total least-squares problem
Signal Processing
Numerical optimization in hybrid symbolic-numeric computation
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Robust counterparts of errors-in-variables problems
Computational Statistics & Data Analysis
Structured total least norm and approximate GCDs of inexact polynomials
Journal of Computational and Applied Mathematics
Solving polynomial systems via symbolic-numeric reduction to geometric involutive form
Journal of Symbolic Computation
High-performance numerical algorithms and software for structured total least squares
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Robustness of a discrete dynamical process with a given set of attainability
Journal of Computer and Systems Sciences International
Structured Total Maximum Likelihood: An Alternative to Structured Total Least Squares
SIAM Journal on Matrix Analysis and Applications
The computation of multiple roots of a polynomial
Journal of Computational and Applied Mathematics
Univariate polynomial root-finding by arming with constraints
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Journal of Computational and Applied Mathematics
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A new formulation and algorithm is described for computing the solution to an overdetermined linear system, $Ax \approx b$, with possible errors in both $A$ and $b$. This approach preserves any affine structure of $A$ or $[A \:|\:b]$, such as Toeplitz or sparse structure, and minimizes a measure of error in the discrete $L_p$ norm, where $p=1,2$, or $\infty$. It can be considered as a generalization of total least squares and we call it structured total least norm (STLN). The STLN problem is formulated, the algorithm for its solution is presented and analyzed, and computational results that illustrate the algorithm convergence and performance on a variety of structured problems are summarized. For each test problem, the solutions obtained by least squares, total least squares, and STLN with $p = 1,2,$ and $\infty$ were compared. These results confirm that the STLN algorithm is an effective method for solving problems where $A$ or $b$ has a special structure or where errors can occur in only some of the elements of $A$ and $b$.