Randomized extended Kaczmarz for solving least squares

Anastasios Zouzias, Nikolaos Freris

    Research output: Contribution to journalArticle

    Abstract

    We present a randomized iterative algorithm that exponentially converges in the mean square to the minimum ℓ2-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.

    Original languageEnglish (US)
    Pages (from-to)773-793
    Number of pages21
    JournalSIAM Journal on Matrix Analysis and Applications
    Volume34
    Issue number2
    DOIs
    StatePublished - Jul 29 2013

    Fingerprint

    Least Squares
    Least-squares Solution
    Linear system of equations
    Randomized Algorithms
    Condition number
    Mean Square
    Iterative Algorithm
    Directly proportional
    Converge
    Norm
    Estimate

    Keywords

    • Iterative method
    • LAPACK
    • Linear least squares
    • Minimum-length solution
    • Overdetermined system
    • Random sampling
    • Randomized algorithms
    • Sparse matrix
    • Underdetermined system

    ASJC Scopus subject areas

    • Analysis

    Cite this

    Randomized extended Kaczmarz for solving least squares. / Zouzias, Anastasios; Freris, Nikolaos.

    In: SIAM Journal on Matrix Analysis and Applications, Vol. 34, No. 2, 29.07.2013, p. 773-793.

    Research output: Contribution to journalArticle

    Zouzias, Anastasios ; Freris, Nikolaos. / Randomized extended Kaczmarz for solving least squares. In: SIAM Journal on Matrix Analysis and Applications. 2013 ; Vol. 34, No. 2. pp. 773-793.
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