منابع مشابه
Scaled total least squares fundamentals
The standard approaches to solving overdetermined linear systems Bx ≈ c construct minimal corrections to the vector c and/or the matrix B such that the corrected system is compatible. In ordinary least squares (LS) the correction is restricted to c, while in data least squares (DLS) it is restricted to B. In scaled total least squares (STLS) [22], corrections to both c and B are allowed, and th...
متن کاملBounds for the least squares distance using scaled total least squares
The standard approaches to solving overdetermined linear systems Bx ≈ c construct minimal corrections to the data to make the corrected system compatible. In ordinary least squares (LS) the correction is restricted to the right hand side c, while in scaled total least squares (STLS) [14, 12] corrections to both c and B are allowed, and their relative sizes are determined by a real positive para...
متن کاملBounds for the Least Squares Residual Using Scaled Total Least Squares
The standard approaches to solving overdetermined linear systems Ax ≈ b construct minimal corrections to the data to make the corrected system compatible. In ordinary least squares (LS) the correction is restricted to the right hand side b, while in scaled total least squares (Scaled TLS) [10; 7] corrections to both b and A are allowed, and their relative sizes are determined by a real positive...
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In this paper, we present a rankrevealing two-sided orthogonal decomposition method for solving the STLS problem. An error analysis of the algorithm is given. Our numerical experiments show that this algorithm computes the STLS solution as accurate as the SVD method with less computation.
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In this note, we present two results on the scaled total least squares problem. First, we discuss the relation between the scaled total least squares and the least squares problems. We derive an upper bound for the difference between the scaled total least squares solution and the least squares solution and establish a quantitative relation between the scaled total least squares residual and th...
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ژورنال
عنوان ژورنال: Numerische Mathematik
سال: 2002
ISSN: 0029-599X,0945-3245
DOI: 10.1007/s002110100314