SIAM Journal on Matrix Analysis and Applications
The restricted singular value decomposition of matrix triplets
SIAM Journal on Matrix Analysis and Applications
The restricted total least squares problem: formulation, algorithm, and properties
SIAM Journal on Matrix Analysis and Applications
Total Least Norm Formulation and Solution for Structured Problems
SIAM Journal on Matrix Analysis and Applications
A unifying convergence analysis of second-order methods for secular equations
Mathematics of Computation
Fast Structured Total Least Squares Algorithm for Solving the Basic Deconvolution Problem
SIAM Journal on Matrix Analysis and Applications
A Global Solution for the Structured Total Least Squares Problem with Block Circulant Matrices
SIAM Journal on Matrix Analysis and Applications
On the Solution of the Tikhonov Regularization of the Total Least Squares Problem
SIAM Journal on Optimization
The constrained total least squares technique and its applicationsto harmonic superresolution
IEEE Transactions on Signal Processing
Total least squares for affinely structured matrices and the noisyrealization problem
IEEE Transactions on Signal Processing
Structured Total Maximum Likelihood: An Alternative to Structured Total Least Squares
SIAM Journal on Matrix Analysis and Applications
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We present and study the matrix-restricted total least squares (MRTLS) devised to solve linear systems of the form Ax~b where A and b are both subjected to noise and A has errors of the form DEC. D and C are known matrices and E is unknown. We show that the MRTLS problem amounts to solving a problem of minimizing a sum of fractional quadratic terms and a quadratic function and compare it to the related restricted TLS problem of Van Huffel and Zha [The restricted total least squares problem: formulation, algorithm, and properties, SIAM J. Matrix Anal. Appl. 12(2) (1991) 292-309.]. Finally, we present an algorithm for solving the MRTLS, which is based on a reduction to a single-variable minimization problem. This reduction is shown to have the ability of eliminating local optima points.