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    A Globally and Quadratically Convergent Algorithm for Solving Multilinear Systems with M-tensors

    265398.pdf (426.3Kb)
    Access Status
    Open access
    Authors
    He, H.
    Ling, C.
    Qi, L.
    Zhou, Guanglu
    Date
    2018
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    He, H. and Ling, C. and Qi, L. and Zhou, G. 2018. A Globally and Quadratically Convergent Algorithm for Solving Multilinear Systems with M-tensors. Journal of Scientific Computing. 76 (3): pp. 1718–1741.
    Source Title
    Journal of Scientific Computing
    DOI
    10.1007/s10915-018-0689-7
    ISSN
    0885-7474
    School
    School of Electrical Engineering, Computing and Mathematical Science (EECMS)
    Remarks

    The final publication is available at Springer via 10.1007/s10915-018-0689-7

    URI
    http://hdl.handle.net/20.500.11937/67006
    Collection
    • Curtin Research Publications
    Abstract

    We consider multilinear systems of equations whose coefficient tensors are (Formula presented.)-tensors. Multilinear systems of equations have many applications in engineering and scientific computing, such as data mining and numerical partial differential equations. In this paper, we show that solving multilinear systems with (Formula presented.)-tensors is equivalent to solving nonlinear systems of equations where the involving functions are P-functions. Based on this result, we propose a Newton-type method to solve multilinear systems with (Formula presented.)-tensors. For a multilinear system with a nonsingular (Formula presented.)-tensor and a positive right side vector, we prove that the sequence generated by the proposed method converges to the unique solution of the multilinear system and the convergence rate is quadratic. Numerical results are reported to show that the proposed method is promising.

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