597 research outputs found

    A literature survey of low-rank tensor approximation techniques

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    During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable by classical techniques. This survey attempts to give a literature overview of current developments in this area, with an emphasis on function-related tensors

    A Distributed and Incremental SVD Algorithm for Agglomerative Data Analysis on Large Networks

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    In this paper, we show that the SVD of a matrix can be constructed efficiently in a hierarchical approach. Our algorithm is proven to recover the singular values and left singular vectors if the rank of the input matrix AA is known. Further, the hierarchical algorithm can be used to recover the dd largest singular values and left singular vectors with bounded error. We also show that the proposed method is stable with respect to roundoff errors or corruption of the original matrix entries. Numerical experiments validate the proposed algorithms and parallel cost analysis
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