Proximity of Weighted and Layered Least Squares Solutions

In this paper, the researchers analyze the limiting behavior of the weighted least squares problem ..., where each ... is a positive definite diagonal matrix. they consider the situation where the magnitude of the weights differs drastically from one block to the next so that ... Here max(...) and m...

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Vydáno v:SIAM journal on matrix analysis and applications Ročník 31; číslo 3; s. 1172 - 1186
Hlavní autoři: Kitahara, Tomonari, Tsuchiya, Takashi
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2009
Témata:
Algebra
Blocking
Constraining
Exact sciences and technology
Infinity
Least squares method
Linear and multilinear algebra, matrix theory
Linear programming
Mathematics
Matrix
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Proximity
Sciences and techniques of general use
Studies
Symbols
Minimum
Proximity
65K05
interior-point methods
Least squares problem
Interior point method
Error bound
Linear programming
layered least squares method
Layer
Bounded solution
Maximum
Numerical analysis
weighted least squares method
Least squares method
93E24
Linear algebra
Positive definite matrix
Condition number
Behavior
65F05
ISSN:0895-4798, 1095-7162
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Popis
Shrnutí:In this paper, the researchers analyze the limiting behavior of the weighted least squares problem ..., where each ... is a positive definite diagonal matrix. they consider the situation where the magnitude of the weights differs drastically from one block to the next so that ... Here max(...) and min(...) represent the maximum and minimum entries of diagonal elements, respectively. Specifically, they consider the case when the gap ... is very large or tends to infinity. Vavasis and Ye proved that the limiting solution exists (when the proportion of diagonal elements within each block ... is unchanged and only the gap g tends to ∞), and showed that the limit is characterized as the solution of a variant of the least squares problem called the layered least squares problem.(ProQuest: ... denotes formulae/symbols omitted.)
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ISSN:0895-4798
1095-7162
DOI:10.1137/080725787