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 in:SIAM journal on matrix analysis and applications 2010-01, Vol.31 (5), p.2769-2783
Main Authors: BÜRGISSER, Peter, CUCKER, Felipe
Format: Article
Language:English
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
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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]
ISSN:0895-4798
1095-7162
DOI:10.1137/100782954