Orthogonal projection and total least squares
نویسندگان
چکیده
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, ...
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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, motivated by structured data matrices occurring in signal and image processing, systems and control, and computer algebra; 3. the use of regularization in the problem for...
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Since there are more equations than unknowns (m > n), this is an overdetermined set of equations. If the measurements of the independent variables xi are known precisely, then the only difference between the model, ŷ(xi; a), and the measured data yi, must be due to measurement error in yi and natural variability in the data that the model is unable to reflect. In such cases, the ‘best’ approxim...
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ژورنال
عنوان ژورنال: Numerical Linear Algebra with Applications
سال: 1995
ISSN: 1070-5325,1099-1506
DOI: 10.1002/nla.1680020206