Functions of Matrices: Theory and Computation

Does averaging overestimate or underestimate population growth? It depends

Logofet, D. O. (2019) · Ecological Modelling · doi:10.1016/j.ecolmodel.2019.108744 · Cited by 14

Eternal adiabaticity in quantum evolution

Burgarth, D. K., Paolo Facchi, A., Nakazato, H., Pascazio, S., & Yuasa, K. (2021) · Physical Review A · doi:10.1103/physreva.103.032214 · Cited by 14

Manifold Gradient Descent Solves Multi-Channel Sparse Blind Deconvolution Provably and Efficiently

Shi, L., & Chi, Y. (2021) · IEEE Transactions on Information Theory · doi:10.1109/tit.2021.3075148 · Cited by 14

Residual and Restarting in Krylov Subspace Evaluation of the $\varphi$ Function

Botchev, M. A., Knizhnerman, L., & Tyrtyshnikov, E. E. (2021) · SIAM Journal on Scientific Computing · doi:10.1137/20m1375383 · Cited by 14

Condition numbers for the nonlinear matrix equation and their statistical estimation

Wang, S., Yang, H., & Li, H. (2015) · Linear Algebra and its Applications · doi:10.1016/j.laa.2015.06.011 · Cited by 14

Computing enclosures for the inverse square root and the sign function of a matrix

Frommer, A., Hashemi, B., & Sablik, T. (2013) · Linear Algebra and its Applications · doi:10.1016/j.laa.2013.11.047 · Cited by 14

spMC: Modelling Spatial Random Fields with Continuous Lag Markov Chains

Sartore, L. (2013) · The R Journal · doi:10.32614/rj-2013-022 · Cited by 14

How to solve the matrix equation XA-AX=f(X)

Bourgeois, G. (2010) · Linear Algebra and its Applications · doi:10.1016/j.laa.2010.09.037 · Cited by 14

Faster Principal Component Regression and Stable Matrix Chebyshev ApproximationPreprint

Allen-Zhu, Z., & Li, Y. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1608.04773 · Cited by 14

Stochastic Climate TheoryPreprint

Gottwald, G. A., Crommelin, D. T., & Franzke, C. L. E. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1612.07474 · Cited by 14

Efficient computation with structured matrices and arithmetic expressions

Mouilleron, C. (2011) · theses.fr (ABES) · doi:10.70675/2bd37edcz2b83z4cb5z97ebz3c7d221f9fa9 · Cited by 14

Impact of the form of weighted networks on the quantum extreme reservoir computation

Hayashi, A., Sakurai, A., Nishio, S., Munro, W. J., & Nemoto, K. (2023) · Physical Review A · doi:10.1103/physreva.108.042609 · Cited by 13

An inexact shift‐and‐invert Arnoldi algorithm for Toeplitz matrix exponential

Wu, G., Feng, T.-T., & Wei, Y. (2015) · Numerical Linear Algebra with Applications · doi:10.1002/nla.1992 · Cited by 13

Numerical approximation to the fractional derivative operator

Novati, P. (2013) · Numerische Mathematik · doi:10.1007/s00211-013-0596-7 · Cited by 13

Quantum fidelity for analyzing atoms and fragments in molecule: Application to similarity, chirality, and aromaticity

Luzanov, A. V. (2010) · International Journal of Quantum Chemistry · doi:10.1002/qua.22510 · Cited by 14

Continuous to discrete model conversion for the system with a singular system matrix based on matrix sign function

Tsai, J. S.-H., Huang, C., Guo, S., & Shieh, L. (2011) · Applied Mathematical Modelling · doi:10.1016/j.apm.2011.02.009 · Cited by 13

Concavity of the Auxiliary Function for Classical-Quantum Channels

Cheng, H.-C., & Hsieh, M.-H. (2016) · IEEE Transactions on Information Theory · doi:10.1109/tit.2016.2598835 · Cited by 13

Preconditioned eigensolvers for large-scale nonlinear Hermitian eigenproblems with variational characterizations. I. Extreme eigenvalues

Szyld, D. B., & Xue, F. (2015) · Mathematics of Computation · doi:10.1090/mcom/3083 · Cited by 13

On the “spin connection foam” picture of quantum gravity from precanonical quantization

Kanatchikov, I. V. (2017) · The Ninth Marcel Grossmann Meeting · doi:10.1142/9789813226609_0519 · Cited by 13

Riemannian Laplace Distribution on the Space of Symmetric Positive Definite Matrices

Hajri, H., Ilea, I., Said, S., Bombrun, L., & Berthoumieu, Y. (2016) · Entropy · doi:10.3390/e18030098 · Cited by 13

Evolutionary image composition using feature covariance matrices

Neumann, A., Szpak, Z. L., Chojnacki, W., & Neumann, F. (2017) · Genetic and Evolutionary Computation Conference (GECCO) · doi:10.1145/3071178.3071260 · Cited by 13

A Numerical Study of the Homogeneous Elliptic Equation with Fractional Boundary Conditions

Lazarov, R., & Vabishchevich, P. N. (2017) · Fractional Calculus and Applied Analysis · doi:10.1515/fca-2017-0018 · Cited by 13

Static elastic cloaking, low-frequency elastic wave transparency and neutral inclusions

Norris, A. N., & Parnell, W. J. (2020) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2019.0725 · Cited by 13

Beyond non-backtracking: non-cycling network centrality measures

Arrigo, F., Higham, D. J., & Noferini, V. (2020) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2019.0653 · Cited by 13

Calculating the divided differences of the exponential function by addition and removal of inputs

Gupta, L., Barash, L., & Hen, I. (2020) · Computer Physics Communications · doi:10.1016/j.cpc.2020.107385 · Cited by 13

Weighted data spaces for correlation-based array imaging in experimental aeroacoustics

Raumer, H.-G., Spehr, C., Hohage, T., & Ernst, D. (2020) · Journal of Sound and Vibration · doi:10.1016/j.jsv.2020.115878 · Cited by 13

A Multiparametric Class of Low-complexity Transforms for Image and Video Coding

Canterle, D. R., da Silveira, T. L. T., Bayer, F. M., & Cintra, R. J. (2020) · Signal Processing · doi:10.1016/j.sigpro.2020.107685 · Cited by 13

Semi-supervised Learning for Aggregated Multilayer Graphs Using Diffuse Interface Methods and Fast Matrix-Vector Products

Bergermann, K., Stoll, M., & Volkmer, T. (2021) · SIAM Journal on Mathematics of Data Science · doi:10.1137/20m1352028 · Cited by 13

Low-Rank Updates of Matrix Functions II: Rational Krylov Methods

Beckermann, B., Cortinovis, A., Kreßner, D., & Schweitzer, M. (2021) · SIAM Journal on Numerical Analysis · doi:10.1137/20m1362553 · Cited by 13

Linnea

Barthels, H., Psarras, C., & Bientinesi, P. (2021) · ACM Transactions on Mathematical Software · doi:10.1145/3446632 · Cited by 13

On the interpolation of calibration solutions obtained in radio interferometry

Yatawatta, S. (2012) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/sts069 · Cited by 13

Approximation of Semigroups and Related Operator Functions by Resolvent Series

Grimm, V., & Gugat, M. (2010) · SIAM Journal on Numerical Analysis · doi:10.1137/090768084 · Cited by 13

Computing matrix functions solving coupled differential models

Defez, E., Sastre, J., Ibáñez, J., & Ruiz, P. A. (2009) · Mathematical and Computer Modelling · doi:10.1016/j.mcm.2009.05.012 · Cited by 13

Efficient and accurate algorithms for computing matrix trigonometric functions

Alonso, P., Ibáñez, J., Sastre, J., Peinado, J., & Defez, E. (2016) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2016.05.015 · Cited by 13

Interpolation on Symmetric Spaces Via the Generalized Polar Decomposition

Gawlik, E. S., & Leok, M. B.-T. (2017) · Foundations of Computational Mathematics · doi:10.1007/s10208-017-9353-0 · Cited by 13

Perturbations and projections of Kalman–Bucy semigroups

Bishop, A. N., Moral, P. D., & Pathiraja, S. (2017) · Stochastic Processes and their Applications · doi:10.1016/j.spa.2017.10.006 · Cited by 13

Computing project makespan distributions: Markovian PERT networks revisited

Burgelman, J., & Vanhoucke, M. (2018) · Computers & Operations Research · doi:10.1016/j.cor.2018.10.017 · Cited by 13

Mixed states in one spatial dimension: Decompositions and correspondence with nonnegative matrices

Cuevas, G. D. L., & Netzer, T. (2020) · Journal of Mathematical Physics · doi:10.1063/1.5127668 · Cited by 13

A Lanczos-like method for non-autonomous linear ordinary differential equations

Giscard, P.-L., & Pozza, S. (2020) · Bollettino Della Unione Matematica Italiana · doi:10.1007/s40574-022-00328-6 · Cited by 13

Notes on Markov embedding

Baake, M., & Sumner, J. G. (2020) · Linear Algebra and its Applications · doi:10.1016/j.laa.2020.02.016 · Cited by 13

Exponential sparsity preserving projection with applications to image recognition

Wei, W., Dai, H., & Liang, W. (2020) · Pattern Recognition · doi:10.1016/j.patcog.2020.107357 · Cited by 13

Counter‐Credit‐Risk Yield Spreads: A Puzzle in China's Corporate Bond Market

Luo, J. H., Ye, X., & Hu, M. (2016) · International Review of Finance · doi:10.1111/irfi.12079 · Cited by 13

Anymatrix: an extensible MATLAB matrix collection

Higham, N. J., & Mikaitis, M. (2021) · Numerical Algorithms · doi:10.1007/s11075-021-01226-2 · Cited by 13

Low Phase-Rank Approximation

Zhao, D., Ringh, A., Qiu, L., & Khong, S. Z. (2022) · Linear Algebra and its Applications · doi:10.1016/j.laa.2022.01.003 · Cited by 13

Monotone convergence of Newton-like methods for M-matrix algebraic Riccati equations

Guo, C. (2012) · Numerical Algorithms · doi:10.1007/s11075-012-9666-7 · Cited by 13

Two-level finite difference scheme of improved accuracy order for time-dependent problems of mathematical physics

Vabishchevich, P. N. (2010) · Computational Mathematics and Mathematical Physics · doi:10.1134/s0965542510010100 · Cited by 13

How long does it take to compute the eigenvalues of a random, symmetric matrix?Preprint

Menon, G. (2017) · arXiv (Cornell University) · doi:10.14288/1.0319078 · Cited by 13

expm: Matrix Exponential, Log, 'etc'

Maechler, M., Dutang, C., & Goulet, V. (2010) · doi:10.32614/cran.package.expm · Cited by 13

Real-variable characterizations and their applications of matrix-weighted Besov spaces on spaces of homogeneous type

Bu, F., Yang, D., & Yuan, W. (2023) · Mathematische Zeitschrift · doi:10.1007/s00209-023-03336-0 · Cited by 12

Thermodynamic matrix exponentials and thermodynamic parallelism

Duffield, S., Aifer, M., Crooks, G. E., Ahle, T. D., & Coles, P. J. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.013147 · Cited by 12

Secrecy in MIMOME wiretap channels: Beamforming with imperfect CSI

Liu, C., Yang, N., Geraci, G., Yuan, J., & Malaney, R. (2014) · International Conference on Communications · doi:10.1109/icc.2014.6884065 · Cited by 12

Computing the Square Roots of a Class of Circulant Matrices

Mei, Y. (2012) · Journal of Applied Mathematics · doi:10.1155/2012/647623 · Cited by 12

On computing complex square roots of real matrices

Liu, Z., Zhang, Y., dos Santos, J. F., & Ralha, R. (2012) · Applied Mathematics Letters · doi:10.1016/j.aml.2012.01.015 · Cited by 12

Why Do Field-Based Methods Fail to Model Plasmonics?

Said, A. M. A., Heikal, A. M., Areed, N. F. F., & Obayya, S. S. A. (2016) · IEEE photonics journal · doi:10.1109/jphot.2016.2600367 · Cited by 12

The Radau--Lanczos Method for Matrix Functions

Frommer, A., Lund, K., Schweitzer, M., & Szyld, D. B. (2017) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/16m1072565 · Cited by 12

Convergence Issues in the Estimation of Interchannel Correlated Observation Errors in Infrared Radiance Data

Gauthier, P., Du, P., Heilliette, S., & Garand, L. (2018) · Monthly Weather Review · doi:10.1175/mwr-d-17-0273.1 · Cited by 12

On Bernoulli matrix polynomials and matrix exponential approximation

Defez, E., Ibáñez, J., Alonso, P., Alonso, J. M., & Peinado, J. (2020) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2020.113207 · Cited by 12

A randomized exponential canonical correlation analysis method for data analysis and dimensionality reduction

Wu, G., & Li, F. (2020) · Applied Numerical Mathematics · doi:10.1016/j.apnum.2020.09.013 · Cited by 12

Probabilistic Rounding Error Analysis of Householder QR Factorization

Connolly, M. P., & Higham, N. J. (2023) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/22m1514817 · Cited by 12

Matrix roots of imprimitive irreducible nonnegative matrices

McDonald, J. J., & Paparella, P. (2015) · Linear Algebra and its Applications · doi:10.1016/j.laa.2015.06.005 · Cited by 12

Extrinsic Mean of Brownian Distributions on Compact Lie Groups

Said, S., & Manton, J. H. (2012) · IEEE Transactions on Information Theory · doi:10.1109/tit.2012.2185680 · Cited by 12

The Padé iterations for the matrix sign function and their reciprocals are optimal

Greco, F., Iannazzo, B., & Poloni, F. (2011) · Linear Algebra and its Applications · doi:10.1016/j.laa.2011.04.016 · Cited by 12

An Accurate Polynomial Approximation of Exponential Integrators

Suhov, A. (2013) · Journal of Scientific Computing · doi:10.1007/s10915-013-9813-x · Cited by 12

Impact of class imbalance on personalized program guide performance

Krstić, M., & Bjelica, M. (2015) · IEEE Transactions on Consumer Electronics · doi:10.1109/tce.2015.7064115 · Cited by 12

A Novel Iterative Method for Polar Decomposition and Matrix Sign Function

Soleymani, F., Stanimirović, P. S., & Stojanović, I. (2015) · Discrete Dynamics in Nature and Society · doi:10.1155/2015/649423 · Cited by 12

Accuracy of singular vectors obtained by projection-based SVD methods

Nakatsukasa, Y. (2017) · BIT Numerical Mathematics · doi:10.1007/s10543-017-0665-x · Cited by 12

Circulant preconditioners for analytic functions of Toeplitz matrices

Hon, S., & Wathen, A. (2018) · Numerical Algorithms · doi:10.1007/s11075-018-0481-7 · Cited by 12

Incrementally updating Katz centrality in dynamic graphs

Nathan, E., & Bader, D. A. (2018) · Social Network Analysis and Mining · doi:10.1007/s13278-018-0504-3 · Cited by 12

Quantum algorithm for matrix functions by Cauchy's integral formula

Takahira, S., Ohashi, A., Sogabe, T., & Usuda, T. S. (2020) · Quantum Information and Computation · doi:10.26421/qic20.1-2-2 · Cited by 12

A residual recurrence for Halley’s method for the matrix p th root

Lin, M. (2010) · Linear Algebra and its Applications · doi:10.1016/j.laa.2009.12.035 · Cited by 12

Embeddability of Kimura 3ST Markov matrices

Roca-Lacostena, J., & Fernández-Sánchez, J. (2018) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2018.02.005 · Cited by 12

Iterative methods for finding commuting solutions of the Yang–Baxter-like matrix equation

Kumar, A., & Cardoso, J. R. (2018) · Applied Mathematics and Computation · doi:10.1016/j.amc.2018.03.078 · Cited by 12

European option valuation under the Bates PIDE in finance: A numerical implementation of the Gaussian scheme

Soleymani, F., & Akgül, A. (2019) · Discrete and Continuous Dynamical Systems - S · doi:10.3934/dcdss.2020052 · Cited by 12

A Monte Carlo method for computing the action of a matrix exponential on a vector

Acebrón, J. A. (2019) · Applied Mathematics and Computation · doi:10.1016/j.amc.2019.06.059 · Cited by 12

A Parallel Overlapping Time-Domain Decomposition Method for ODEs

Güttel, S. (2013) · Lecture notes in computational science and engineering · doi:10.1007/978-3-642-35275-1_54 · Cited by 12

Numerical methods for large Lyapunov equations

Mikkelsen, C. C. K. (2009) · Purdue e-Pubs (Purdue University System) · Cited by 12

Preconditioned iterative methods for inhomogeneous acoustic scattering applications

Sifuentes, J. (2010) · Rice Research Repository (Rice University) · Cited by 12

A Krylov Subspace Method for Option PricingPreprint

Niesen, J., & Wright, W. M. (2011) · SSRN Electronic Journal · doi:10.2139/ssrn.1799124 · Cited by 12

Advanced Optimal Control Methods for Spin Systems

Goodwin, D. L. (2017) · ePrints Soton (University of Southampton) · doi:10.5258/soton/t0003 · Cited by 12

Computing the Action of Trigonometric and Hyperbolic Matrix FunctionsPreprint

Higham, N. J., & Kandolf, P. (2016) · MIMS EPrints (University of Southampton) · Cited by 12

Revising the Boundary Element Method for Thermoviscous Acoustics: An Iterative Approach via Schur Complement

Preuss, S., Paltorp, M., Blanc, A., Henrı́quez, V. C., & Marburg, S. (2023) · Journal of Theoretical and Computational Acoustics · doi:10.1142/s2591728523500159 · Cited by 11

The Comparison of Riemannian Geometric Matrix-CFAR Signal Detectors

Ono, Y., & Peng, L. (2023) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2023.3339403 · Cited by 11

A theoretical analysis of mass scaling techniques

Voet, Y., Sande, E., & Buffa, A. (2025) · Computational Mechanics · doi:10.1007/s00466-025-02611-7 · Cited by 11

Some remarks on the monotonicity of primary matrix functions on the set of symmetric matrices

Martin, R. J., & Neff, P. (2015) · Archive of Applied Mechanics · doi:10.1007/s00419-015-1017-4 · Cited by 11

Standard Codon Substitution Models Overestimate Purifying Selection for Non-Stationary Data

Kaehler, B. D., Yap, V. B., & Huttley, G. A. (2017) · Genome Biology and Evolution · doi:10.1093/gbe/evw308 · Cited by 11

Generalized Locally Toeplitz Sequences: A Spectral Analysis Tool for Discretized Differential Equations

Garoni, C., & Serra‐Capizzano, S. (2018) · Lecture notes in mathematics · doi:10.1007/978-3-319-94911-6_3 · Cited by 11

Centrality Measures Based on Matrix Functions

Njotto, L. L. (2018) · Open Journal of Discrete Mathematics · doi:10.4236/ojdm.2018.84008 · Cited by 11

Procrustes problems in Riemannian manifolds of positive definite matrices

Bhatia, R., & Congedo, M. (2018) · Linear Algebra and its Applications · doi:10.1016/j.laa.2018.11.009 · Cited by 11

Conditional Simulation of Spatially Varying Multicomponent Nonstationary Ground Motions: Bias and Ill Condition

Cui, X. Z., & HONG, H. P. (2019) · Journal of Engineering Mechanics · doi:10.1061/(asce)em.1943-7889.0001700 · Cited by 11

Iterative algorithms for the post-processing of high-dimensional data

Espig, M., Hackbusch, W., Litvinenko, A., Matthies, H. G., & Zander, E. (2020) · Journal of Computational Physics · doi:10.1016/j.jcp.2020.109396 · Cited by 11

Computing the matrix geometric mean: Riemannian versus Euclidean conditioning, implementation techniques, and a Riemannian BFGS method

Yuan, X., Huang, W. T., Absil, P.-A., & Gallivan, K. A. (2020) · Numerical Linear Algebra with Applications · doi:10.1002/nla.2321 · Cited by 11

Riemannian Gaussian distributions, random matrix ensembles and diffusion kernels

Santilli, L., & Tierz, M. (2021) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2021.115582 · Cited by 11

Weighted MPCEP Inverse of an Operator Between Hilbert Spaces

Stojanović, K. S., & Mosić, D. (2021) · Bulletin of the Iranian Mathematical Society. · doi:10.1007/s41980-020-00501-7 · Cited by 11

On Behavior Laplace Integral Operators with Generalized Bessel Matrix Polynomials and Related Functions

Hidan, M., Akel, M. S., Boulaaras, S., & Abdalla, M. (2021) · Journal of Function Spaces · doi:10.1155/2021/9967855 · Cited by 11

Auxiliary task guided mean and covariance alignment network for adversarial domain adaptation

Qiang, W., Li, J., Zheng, C., & Su, B. (2021) · Knowledge-Based Systems · doi:10.1016/j.knosys.2021.107066 · Cited by 11

Perturbation Theory for Quantum Information

Grace, M. R., & Guha, S. (2022) · IEEE Information Theory Workshop (ITW) · doi:10.1109/itw54588.2022.9965836 · Cited by 11

On stochasticity preserving methods for the computation of the matrix pth root

Politi, T., & Popolizio, M. (2014) · Mathematics and Computers in Simulation · doi:10.1016/j.matcom.2014.01.002 · Cited by 11

A short guide to exponential Krylov subspace time integration for Maxwell's equations

Botchev, M. A. (2012) · Cited by 11

On a fourth-order matrix method for computing polar decomposition

Haghani, F. K., & Soleymani, F. (2014) · Computational and Applied Mathematics · doi:10.1007/s40314-014-0124-0 · Cited by 11

Stochastic differential equation systems for an SIS epidemic model with vaccination and immigration

Farnoosh, R., & Parsamanesh, M. (2016) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2016.1189571 · Cited by 11

Computing matrix functions

Higham, N. J., & Al-Mohy, A. H. (2010) · Acta Numerica · doi:10.1017/s0962492910000036 · Cited by 104

4. Techniques for General Functions

Higham, N. J. (2008) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898717778.ch4

Condition Estimation for Matrix Functions via the Schur Decomposition

Mathias, R. (1995) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479893244389 · Cited by 21

Algorithms for Matrix Functions and their Frechet Derivatives and Condition Numbers

Relton, S. D. (2014) · MIMS EPrints (University of Southampton) · Cited by 1

Condition numbers for functions of matrices

Gohberg, I., & Koltracht, I. (1993) · Applied Numerical Mathematics · doi:10.1016/0168-9274(93)90114-7 · Cited by 4