منابع مشابه
Unifying Least Squares, Total Least Squares and Data Least Squares
The standard approaches to solving overdetermined linear systems Ax ≈ b construct minimal corrections to the vector b and/or the matrix A such that the corrected system is compatible. In ordinary least squares (LS) the correction is restricted to b, while in data least squares (DLS) it is restricted to A. In scaled total least squares (Scaled TLS) [15], corrections to both b and A are allowed, ...
متن کاملThe matrix-restricted total least-squares problem
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...
متن کاملGeneralizations of the total least squares problem
Recent advances in total least squares approaches for solving various errorsin-variables modeling problems are reviewed, with emphasis on the following generalizations: 1. the use of weighted norms as a measure of the data perturbation size, capturing prior knowledge about uncertainty in the data; 2. the addition of constraints on the perturbation to preserve the structure of the data matrix, m...
متن کاملA Linearly Constrained Least-squares Problem in Electronic Structure Computations
Abstract. One of the fundamental problems in electronic structure calculations is to determine the electron density associated with the minimum total energy of a molecular or bulk system. The total energy minimization problem is often formulated as a nonlinear eigenvalue problem. The most widely used algorithm for solving this type of problem is the self-consistent field (SCF) iteration acceler...
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ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1937
ISSN: 0003-4851
DOI: 10.1214/aoms/1177732410