Journal
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
Volume 34, Issue 2, Pages 773-793Publisher
SIAM PUBLICATIONS
DOI: 10.1137/120889897
Keywords
linear least squares; minimum-length solution; sparse matrix; overdetermined system; underdetermined system; iterative method; random sampling; LAPACK; randomized algorithms
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Funding
- Qualcomm Inc.
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We present a randomized iterative algorithm that exponentially converges in the mean square to the minimum l(2)-norm least squares solution of a given linear system of equations. The expected number of arithmetic operations required to obtain an estimate of given accuracy is proportional to the squared condition number of the system multiplied by the number of nonzero entries of the input matrix. The proposed algorithm is an extension of the randomized Kaczmarz method that was analyzed by Strohmer and Vershynin.
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