Publications | Xiaobo Liu

Matrix Functions

A scaling and recovering algorithm for the matrix \(\varphi\)-functions (with A. H. Al-Mohy). SIAM J. Sci. Comput., 48(2):A726-A747, 2026.

[BibTeX]

@article{alli26,
  author = "Awad H. Al-Mohy and Xiaobo Liu",
  title = "A scaling and recovering algorithm for the matrix $\varphi$-functions",
  journal = "SIAM J. Sci. Comput.",
  volume = 48,
  number = 2,
  pages = "A726-A747",
  year = 2026,
  doi = "10.1137/25M1765262"
}

Computing the square root of a low-rank perturbation of the scaled identity matrix (with M. Fasi and N. J. Higham). SIAM J. Matrix Anal. Appl., 44(1):156-174, 2023.

[BibTeX]

@article{fhl23,
  author = "Massimiliano Fasi and Nicholas J. Higham and Xiaobo Liu",
  title = "Computing the square root of a low-rank perturbation of the
           scaled identity matrix",
  journal = "SIAM J. Matrix Anal. Appl.",
  volume = 44,
  number = 1,
  pages = "156-174",
  year = 2023,
  doi = "10.1137/22M1471559"
}

Arbitrary precision algorithms for computing the matrix cosine and its Fréchet derivative (with A. H. Al-Mohy and N. J. Higham). SIAM J. Matrix Anal. Appl., 43(1):233-256, 2022.

[BibTeX]

@article{ahl22,
  author = "Awad H. Al-Mohy and Nicholas J. Higham and Xiaobo Liu",
  title = "Arbitrary precision algorithms for computing the matrix cosine
           and its {Fr\'echet} derivative",
  journal = "SIAM J. Matrix Anal. Appl.",
  volume = 43,
  number = 1,
  pages = "233-256",
  year = 2022,
  doi = "10.1137/21m1441043"
}

A multiprecision derivative-free Schur--Parlett algorithm for computing matrix functions (with N. J. Higham). SIAM J. Matrix Anal. Appl., 42(3):1401-1422, 2021.

[BibTeX]

@article{hili21,
  author = "Nicholas J. Higham and Xiaobo Liu",
  title = "A multiprecision derivative-free {Schur--Parlett} algorithm for
           computing matrix functions",
  journal = "SIAM J. Matrix Anal. Appl.",
  volume = 42,
  number = 3,
  pages = "1401-1422",
  year = 2021,
  doi = "10.1137/20m1365326"
}

Computing Matrix Functions in Arbitrary Precision Arithmetic. Ph.D. Thesis, Department of Mathematics, The University of Manchester, Manchester, UK, June 2022.

[BibTeX]

@phdthesis{liu22,
  author = "Xiaobo Liu",
  title = "Computing Matrix Functions in Arbitrary Precision Arithmetic",
  school  = "The University of Manchester",
  address = "Manchester, UK",
  month = jun,
  pages = 157,
  year = 2022,
  url = "https://research.manchester.ac.uk/en/studentTheses/computing-matrix-functions-in-arbitrary-precision-arithmetic-2"
}

Mixed-Precision Methods in Numerical Linear Algebra

Mixed-precision iterative refinement for low-rank Lyapunov equations (with P. Benner). ArXiv:2510.02126 [math.NA], October 2025.

[BibTeX]

@techreport{beli25,
  author = "Peter Benner and Xiaobo Liu",
  title = "Mixed-precision iterative refinement for low-rank {Lyapunov} equations",
  month = oct,
  year = 2025,
  type = "{ArXiv}:2510.02126 [math.{NA}]",
  url = "https://arxiv.org/abs/2510.02126"
}

Mixed-precision algorithms for solving the Sylvester matrix equation (with A. Dmytryshyn, M. Fasi, and N. J. Higham). ArXiv:2503.03456 [math.NA], March 2025; revised March 2026.

[BibTeX]

@techreport{dfhl25,
  author = "Andrii Dmytryshyn and Massimiliano Fasi and Nicholas J. Higham and Xiaobo Liu",
  title = "Mixed-precision algorithms for solving the {Sylvester} matrix equation",
  month = mar,
  year = 2025,
  type = "{ArXiv}:2503.03456 [math.{NA}]",
  url = "https://arxiv.org/abs/2503.03456v2",
  note = "Revised March 2026"
}

Mixed precision HODLR matrices (with E. Carson and X. Chen). SIAM J. Sci. Comput., 47(3):A1408-A1435, 2025.

[BibTeX]

@article{ccl25,
  author = "Erin Carson and Xinye Chen and Xiaobo Liu",
  title = "Mixed precision {HODLR} matrices",
  journal = "SIAM J. Sci. Comput.",
  volume = 47,
  number = 3,
  pages = "A1408-A1435",
  year = 2025,
  doi = "10.1137/24M1683925"
}

Mixed-precision Paterson--Stockmeyer method for evaluating polynomials of matrices. SIAM J. Matrix Anal. Appl., 46(1):811-835, 2025.

[BibTeX]

@article{liu25,
  author = "Xiaobo Liu",
  title = "Mixed-precision {Paterson--Stockmeyer} method for evaluating polynomials of matrices",
  journal = "SIAM J. Matrix Anal. Appl.",
  volume = 46,
  number = 1,
  pages = "811-835",
  year = 2025,
  doi = "10.1137/24M1675734"
}

Low-Rank Matrix Equations

Reduced rank extrapolation for multi-term Sylvester equations (with P. Benner, P. den Boef, P. Kürschner, and J. Saak). ArXiv:2603.12979 [math.NA], March 2026.

[BibTeX]

@techreport{bdkl26,
  author = "Peter Benner and den Boef, Pascal and Patrick K\"{u}rschner and Xiaobo Liu and Jens Saak",
  title = "Reduced rank extrapolation for multi-term {Sylvester} equations",
  month = mar,
  year = 2026,
  type = "{ArXiv}:2603.12979 [math.{NA}]",
  url = "https://arxiv.org/abs/2603.12979"
}

Generalizing reduced rank extrapolation to low-rank matrix sequences (with P. den Boef, P. Kürschner, J. Maubach, J. Saak, W. Schilders, J. Schulze, and N. van de Wouw). ArXiv:2502.09165 [math.NA], February 2025; revised December 2025.

[BibTeX]

@techreport{dklm25,
  author = "den Boef, Pascal and Patrick K\"{u}rschner and Xiaobo Liu and Jos Maubach and Jens Saak and Wil Schilders and Jonas Schulze and van de Wouw, Nathan",
  title = "Generalizing reduced rank extrapolation to low-rank matrix sequences",
  month = feb,
  year = 2025,
  type = "{ArXiv}:2502.09165 [math.{NA}]",
  url = "https://arxiv.org/abs/2502.09165",
  note = "Revised December 2025"
}

Miscellaneous Papers

Computing k-means in mixed precision (with E. Carson and X. Chen). ArXiv:2407.12208 [math.NA], July 2024.

[BibTeX]

@techreport{ccl24,
  author = "Erin Carson and Xinye Chen and Xiaobo Liu",
  title = "Computing $k$-means in mixed precision",
  month = jul,
  year = 2024,
  type = "{ArXiv}:2407.12208 [math.{NA}]",
  url = "https://arxiv.org/abs/2407.12208"
}

A note on the cross matrices. ArXiv:2504.00325 [math.NA], April 2025. MIMS EPrint 2023.1, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, January 2023.

[BibTeX]

@techreport{liu25a,
  author = "Xiaobo Liu",
  title = "A note on the cross matrices",
  month = apr,
  year = 2025,
  type = "{ArXiv}:2504.00325 [math.{NA}]",
  url = "https://arxiv.org/abs/2504.00325",
  note = "MIMS EPrint 2023.1, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, January 2023."
}