Publications

34.

K. Lund and M. Schweitzer, "On the stability of basis construction in extended Krylov subspace methods" , 2026.

DOI: 10.48550/arXiv.2610.21603

33.

X. Liu and M. Schweitzer, "Field-of-values analysis of augmented Krylov methods for matrix $\varphi$-function actions" , 2026.

DOI: 10.48550/arXiv.2607.17819

32.

E. Krieger and M. Schweitzer, "A general framework for Krylov ODE residuals with applications to randomized Krylov methods", Electron. Trans. Numer. Anal., vol. 65, pp. 414-440, 2026.

DOI: 10.1553/etna_vol65s414

31.

M. Hamadi, N. Mahdavi-Amiri and M. Schweitzer, "Splitting methods based on the nonzero diagonal pattern for computing matrix functions" , 2025.

DOI: 10.48550/arXiv.2408.04128

30.

M. Schweitzer, "Near instance optimality of the Lanczos method for Stieltjes and related matrix functions", SIAM J. Matrix Anal. Appl., vol. 46, pp. 1846-1865, 2025.

DOI: 10.1137/25M1739650

29.

D. Palitta, M. Schweitzer and V. Simoncini, "Sketched and truncated polynomial Krylov methods: Evaluation of matrix functions", Numer. Linear Algebra Appl., vol. 32, pp. e2596, 2025.

DOI: 10.1002/nla.2596

28.

A. Frommer, M. Rinelli and M. Schweitzer, "Analysis of stochastic probing methods for estimating the trace of functions of sparse symmetric matrices", Math. Comp., vol. 94, pp. 801-823, 2025.

DOI: https://doi.org/10.1090/mcom/3984

27.

V. Patel, D. A. Maldonado, M. Melnichenko, N. Pritchard, V. Rao, E. Rebrova, S. Sankararaman and M. Schweitzer, "Scientific Applications Leveraging Randomized Linear Algebra" , 2025.

DOI: 10.48550/arXiv.2506.16457

26.

D. Palitta, M. Schweitzer and V. Simoncini, "Sketched and truncated polynomial Krylov subspace methods: Matrix Sylvester equations", Math. Comp., 2024.

DOI: https://doi.org/10.1090/mcom/4002

25.

M. Fasi, S. Gaudreault, K. Lund and M. Schweitzer, "Challenges in computing matrix functions" , 2024.

DOI: 10.48550/arXiv.2401.16132

24.

B. Arslan, S. D. Relton and M. Schweitzer, "Structured level-2 condition numbers of matrix functions", Electron. J. Linear Algebra, vol. 40, pp. 28-47, 2024.

DOI: 10.13001/ela.2024.7905

23.

M. A. Botchev, L. A. Knizhnerman and M. Schweitzer, "Krylov subspace residual and restarting for certain second order differential equations", SIAM J. Sci. Comput., vol. 46, no. 2, pp. S223-S253, 2024.

DOI: 10.1137/22M1503300

22.

A. Frommer, G. Ramirez-Hidalgo, M. Schweitzer and M. Tsolakis, "Polynomial preconditioning for the action of the matrix square root and inverse square root", Electron. Trans. Numer. Anal., vol. 60, pp. 381-404, 2024.

DOI: 10.1553/etna_vol60s381

21.

S. Güttel and M. Schweitzer, "Randomized sketching for Krylov approximations of large-scale matrix functions", SIAM J. Matrix Anal. Appl., vol. 44, pp. 1073-1095, 2023.

DOI: 10.1137/22M1518062

20.

A. Frommer, K. Kahl, M. Schweitzer and M. Tsolakis, "Krylov subspace restarting for matrix Laplace transforms", SIAM J. Matrix Anal. Appl., vol. 44, no. 2, pp. 693-717, 2023.

DOI: 10.1137/22M1499674

19.

M. Schweitzer, "Integral representations for higher-order Frechet derivatives of matrix functions: Quadrature algorithms and new results on the level-2 condition number", Linear Algebra Appl., vol. 656, pp. 247-276, 2023.

DOI: 10.1016/j.laa.2022.10.005

18.

K. Lund and M. Schweitzer, "The Frechet derivative of the tensor t-function", Calcolo, vol. 60, 2023.

DOI: 10.1007/s10092-023-00527-3

17.

M. Schweitzer, "Sensitivity of matrix function based network communicability measures: Computational methods and a priori bounds", SIAM J. Matrix Anal. Appl., vol. 44, no. 3, pp. 1321-1348, 2023.

DOI: 10.1137/23M1556708

16.

M. Schweitzer, "Decay bounds for Bernstein functions of Hermitian matrices with applications to the fractional graph Laplacian", Electron. Trans. Numer. Anal., vol. 55, pp. 438-454, 2022.

DOI: 10.1553/etna_vol55s438

15.

P. Kandolf, A. Koskela, S. D. Relton and M. Schweitzer, "Computing low-rank approximations of the Frechet derivative of a matrix function using Krylov subspace methods", Numer. Linear Algebra Appl., vol. 28, no. 6, pp. e2401, 31, 2021.

DOI: 10.1002/nla.2401

14.

A. Frommer, C. Schimmel and M. Schweitzer, "Analysis of probing techniques for sparse approximation and trace estimation of decaying matrix functions", SIAM J. Matrix Anal. Appl., vol. 42, no. 3, pp. 1290-1318, 2021.

DOI: 10.1137/20M1364461

13.

B. Beckermann, A. Cortinovis, D. Kressner and M. Schweitzer, "Low-rank updates of matrix functions II: Rational Krylov methods", SIAM J. Numer. Anal., vol. 59, no. 3, pp. 1325-1347, 2021.

DOI: 10.1137/20M1362553

12.

S. Güttel and M. Schweitzer, "A comparison of limited-memory Krylov methods for Stieltjes functions of Hermitian matrices", SIAM J. Matrix Anal. Appl., vol. 42, no. 1, pp. 83-107, 2021.

DOI: 10.1137/20M1351072

11.

A. Frommer, C. Schimmel and M. Schweitzer, "Non-Toeplitz decay bounds for inverses of Hermitian positive definite tridiagonal matrices", Electron. Trans. Numer. Anal., vol. 48, pp. 362-372, 2018.

DOI: 10.1553/etna_vol48s362

10.

A. Frommer, C. Schimmel and M. Schweitzer, "Bounds for the decay of the entries in inverses and Cauchy-Stieltjes functions of certain sparse, normal matrices", Numer. Linear Algebra Appl., vol. 25, no. 4, pp. e2131, 17, 2018.

DOI: 10.1002/nla.2131

9.

B. Beckermann, D. Kressner and M. Schweitzer, "Low-rank updates of matrix functions", SIAM J. Matrix Anal. Appl., vol. 39, no. 1, pp. 539-565, 2018.

DOI: 10.1137/17M1140108

8.

M. Schweitzer, "A two-sided short-recurrence extended Krylov subspace method for nonsymmetric matrices and its relation to rational moment matching", Numer. Algorithms, vol. 76, no. 1, pp. 1-31, 2017.

DOI: 10.1007/s11075-016-0239-z

7.

A. Frommer, K. Lund, M. Schweitzer and D. B. Szyld, "The Radau-Lanczos method for matrix functions", SIAM J. Matrix Anal. Appl., vol. 38, no. 3, pp. 710-732, 2017.

DOI: 10.1137/16M1072565

6.

M. Schweitzer, "Restarting and error estimation in polynomial and extended Krylov subspace methods for the approximation of matrix functions", Bergische Universität Wuppertal, Fakultät für Mathematik und Naturwissenschaften, 2016.

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5.

A. Frommer and M. Schweitzer, "Error bounds and estimates for Krylov subspace approximations of Stieltjes matrix functions", BIT, vol. 56, no. 3, pp. 865-892, 2016.

DOI: 10.1007/s10543-015-0596-3

4.

M. Schweitzer, "Monotone convergence of the extended Krylov subspace method for Laplace-Stieltjes functions of Hermitian positive definite matrices", Linear Algebra Appl., vol. 507, pp. 486-498, 2016.

DOI: 10.1016/j.laa.2016.06.041

3.

M. Schweitzer, "Any finite convergence curve is possible in the initial iterations of restarted FOM", Electron. Trans. Numer. Anal., vol. 45, pp. 133-145, 2016.

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2.

A. Frommer, S. Güttel and M. Schweitzer, "Convergence of restarted Krylov subspace methods for Stieltjes functions of matrices", SIAM J. Matrix Anal. Appl., vol. 35, no. 4, pp. 1602-1624, 2014.

DOI: 10.1137/140973463

1.

A. Frommer, S. Güttel and M. Schweitzer, "Efficient and stable Arnoldi restarts for matrix functions based on quadrature", SIAM J. Matrix Anal. Appl., vol. 35, no. 2, pp. 661-683, 2014.

DOI: 10.1137/13093491X