Tikhonov Regularization and Total Least Squares
نویسندگان
چکیده
منابع مشابه
Tikhonov Regularization and Total Least Squares
Discretizations of inverse problems lead to systems of linear equations with a highly ill-conditioned coefficient matrix, and in order to compute stable solutions to these systems it is necessary to apply regularization methods. We show how Tikhonov’s regularization method, which in its original formulation involves a least squares problem, can be recast in a total least squares formulation sui...
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The total least squares (TLS) method is a successful approach for linear problems when not only the right-hand side but the system matrix as well are contaminated by some noise. For ill-posed TLS problems regularization is necessary to stabilize the computed solution. In this paper we present a new approach for computing an approximate solution of the Tikhonov-regularized large-scale total leas...
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In this paper, we study and analyze the regularized weighted total least squares (RWTLS) formulation. Our regularization of the weighted total least squares problem is based on the Tikhonov regularization. Numerical examples are presented to demonstrate the effectiveness of the RWTLS method.
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Total least squares (TLS) is a method for treating an overdetermined system of linear equations Ax ≈ b, where both the matrix A and the vector b are contaminated by noise. Tikhonov regularization of the TLS (TRTLS) leads to an optimization problem of minimizing the sum of fractional quadratic and quadratic functions. As such, the problem is nonconvex. We show how to reduce the problem to a sing...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 1999
ISSN: 0895-4798,1095-7162
DOI: 10.1137/s0895479897326432