SMOOTHED ANALYSIS OF MOORE―PENROSE INVERSION

We perform a smoothed analysis of the condition number of rectangular matrices. We prove that, asymptotically, the expected value of this condition number depends only on the elongation of the matrix and not on the center and variance of the underlying probability distribution. [PUBLICATION ABSTRACT...

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Bibliographic Details
Published inSIAM journal on matrix analysis and applications Vol. 31; no. 5; pp. 2769 - 2783
Main Authors BÜRGISSER, Peter, CUCKER, Felipe
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2010
Subjects
Algebra
Asymptotic properties
Elongation
Exact sciences and technology
Inverse problems
Inversions
Linear and multilinear algebra, matrix theory
Linear inference, regression
Mathematical analysis
Mathematics
Matrices
Matrix
Matrix methods
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Probability and statistics
Probability distribution
Sciences and techniques of general use
Statistics
Studies
Variance
Center
Secondary
smoothed analysis
Inversion
Probability distribution
least-squares
15A09
Moore-Penrose inversion
Variance
Numerical analysis
Least squares method
Linear algebra
Primary
Condition number
Matrices
65F35
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Summary:We perform a smoothed analysis of the condition number of rectangular matrices. We prove that, asymptotically, the expected value of this condition number depends only on the elongation of the matrix and not on the center and variance of the underlying probability distribution. [PUBLICATION ABSTRACT]
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0895-4798
1095-7162
DOI:10.1137/100782954