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Randomized block-Krylov subspace methods for low-rank approximation of matrix functions.

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Title: Randomized block-Krylov subspace methods for low-rank approximation of matrix functions.
Authors: Persson, David1 (AUTHOR) dpersson@flatironinstitute.org, Chen, Tyler2 (AUTHOR) tyler.chen@nyu.edu, Musco, Christopher2 (AUTHOR) cmusco@nyu.edu
Source: Linear Algebra & its Applications. Jul2026, Vol. 741, p32-65. 34p.
Subjects: Matrix functions, Krylov subspace, Singular value decomposition, Approximation theory, Matrix multiplications, Low-rank matrices, Numerical solutions for linear algebra
Abstract: The randomized SVD is a method to compute an inexpensive, yet accurate, low-rank approximation of a matrix. The algorithm assumes access to the matrix through matrix-vector products (matvecs). Therefore, when we would like to apply the randomized SVD to a matrix function, f (A) , one needs to approximate matvecs with f (A) using some other algorithm, which is typically treated as a black-box. Chen and Hallman (SIMAX 2023) argued that, in the common setting where matvecs with f (A) are approximated using Krylov subspace methods (KSMs), a more efficient low-rank approximation is possible if we open this black-box. They present an alternative approach that significantly outperforms the naive combination of KSMs with the randomized SVD, although the method lacked theoretical justification. In this work, we take a closer look at the method, and provide strong and intuitive error bounds that justify its excellent performance for low-rank approximation of matrix functions. [ABSTRACT FROM AUTHOR]
Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 193119970
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  Data: Randomized block-Krylov subspace methods for low-rank approximation of matrix functions.
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  Data: <searchLink fieldCode="JN" term="%22Linear+Algebra+%26+its+Applications%22">Linear Algebra & its Applications</searchLink>. Jul2026, Vol. 741, p32-65. 34p.
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  Data: <searchLink fieldCode="DE" term="%22Matrix+functions%22">Matrix functions</searchLink><br /><searchLink fieldCode="DE" term="%22Krylov+subspace%22">Krylov subspace</searchLink><br /><searchLink fieldCode="DE" term="%22Singular+value+decomposition%22">Singular value decomposition</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+multiplications%22">Matrix multiplications</searchLink><br /><searchLink fieldCode="DE" term="%22Low-rank+matrices%22">Low-rank matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+for+linear+algebra%22">Numerical solutions for linear algebra</searchLink>
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  Data: The randomized SVD is a method to compute an inexpensive, yet accurate, low-rank approximation of a matrix. The algorithm assumes access to the matrix through matrix-vector products (matvecs). Therefore, when we would like to apply the randomized SVD to a matrix function, f (A) , one needs to approximate matvecs with f (A) using some other algorithm, which is typically treated as a black-box. Chen and Hallman (SIMAX 2023) argued that, in the common setting where matvecs with f (A) are approximated using Krylov subspace methods (KSMs), a more efficient low-rank approximation is possible if we open this black-box. They present an alternative approach that significantly outperforms the naive combination of KSMs with the randomized SVD, although the method lacked theoretical justification. In this work, we take a closer look at the method, and provide strong and intuitive error bounds that justify its excellent performance for low-rank approximation of matrix functions. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.laa.2026.03.029
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      – Code: eng
        Text: English
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        PageCount: 34
        StartPage: 32
    Subjects:
      – SubjectFull: Matrix functions
        Type: general
      – SubjectFull: Krylov subspace
        Type: general
      – SubjectFull: Singular value decomposition
        Type: general
      – SubjectFull: Approximation theory
        Type: general
      – SubjectFull: Matrix multiplications
        Type: general
      – SubjectFull: Low-rank matrices
        Type: general
      – SubjectFull: Numerical solutions for linear algebra
        Type: general
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      – TitleFull: Randomized block-Krylov subspace methods for low-rank approximation of matrix functions.
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            NameFull: Chen, Tyler
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            NameFull: Musco, Christopher
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            – D: 15
              M: 07
              Text: Jul2026
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              Y: 2026
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