Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularized Computation of Approximate Pseudoinverse of Large Matrices
  Using Low-Rank Tensor Train Decompositions   We propose a new method for low-rank approximation of Moore-Penrose
pseudoinverses (MPPs) of large-scale matrices using tensor networks. The
computed pseudoinverses can be useful for solving or preconditioning of
large-scale overdetermined or underdetermined systems of linear equations. The
computation is performed efficiently and stably based on the modified
alternating least squares (MALS) scheme using low-rank tensor train (TT)
decompositions and tensor network contractions. The formulated large-scale
optimization problem is reduced to sequential smaller-scale problems for which
any standard and stable algorithms can be applied. Regularization technique is
incorporated in order to alleviate ill-posedness and obtain robust low-rank
approximations. Numerical simulation results illustrate that the regularized
pseudoinverses of a wide class of non-square or nonsymmetric matrices admit
good approximate low-rank TT representations. Moreover, we demonstrated that
the computational cost of the proposed method is only logarithmic in the matrix
size given that the TT-ranks of a data matrix and its approximate pseudoinverse
are bounded. It is illustrated that a strongly nonsymmetric
convection-diffusion problem can be efficiently solved by using the
preconditioners computed by the proposed method.

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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci