Functions of Matrices: Theory and Computation

An example of robust internal model control under variable and uncertain delay

Clerget, C.-H., Grimaldi, J.-P., Chèbre, M., & Petit, N. (2017) · Journal of Process Control · doi:10.1016/j.jprocont.2017.04.003 · Cited by 11

Learning Continuous-Time Hidden Markov Models for Event Data

Liu, Y., Moreno, A., Li, S., Li, F., Song, L., & Rehg, J. M. (2017) · Springer eBooks · doi:10.1007/978-3-319-51394-2_19 · Cited by 11

An approach to H2, model reduction on finite interval for bilinear systems

Xu, K.-L., & Jiang, Y. (2017) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2017.08.037 · Cited by 11

The Structured Condition Number of a Differentiable Map between Matrix Manifolds, with Applications

Arslan, B., Noferini, V., & Françoise Tisseur, B. (2019) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/17m1148943 · Cited by 11

Sensitivity analysis of the recovery time for a population under the impact of an environmental disturbance

Ackleh, A. S., Caswell, H., Chiquet, R. A., Tang, T., & Veprauskas, A. (2018) · Natural Resource Modeling · doi:10.1111/nrm.12166 · Cited by 11

Verified computation of the matrix exponential

Miyajima, S. (2018) · Advances in Computational Mathematics · doi:10.1007/s10444-018-9609-5 · Cited by 11

Approximating the Matrix Exponential of an Advection-Diffusion Operator Using the Incomplete Orthogonalization Method

Koskela, A. (2014) · Lecture notes in computational science and engineering · doi:10.1007/978-3-319-10705-9_34 · Cited by 11

Fast Taylor polynomial evaluation for the computation of the matrix cosine

Sastre, J., Ibáñez, J., Alonso, P., Peinado, J., & Defez, E. (2019) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2018.12.041 · Cited by 11

A highly parallel algorithm for computing the action of a matrix exponential on a vector based on a multilevel Monte Carlo method

Acebrón, J. A., Herrero, J. R., & Monteiro, J. C. (2020) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2020.02.013 · Cited by 11

Splitting schemes for non-stationary problems with a rational approximation for fractional powers of the operator

Vabishchevich, P. N. (2021) · Applied Numerical Mathematics · doi:10.1016/j.apnum.2021.03.006 · Cited by 11

Controlling Errors in Recursive Fermi–Dirac Operator Expansions with Applications in Electronic Structure Theory

Rubensson, E. H. (2012) · SIAM Journal on Scientific Computing · doi:10.1137/11083352x · Cited by 11

Automated parameter selection for rational Arnoldi approximation of Markov functions

Güttel, S., & Knizhnerman, L. (2011) · PAMM · doi:10.1002/pamm.201110005 · Cited by 11

Discontinuous parameter estimates with least squares estimators

Mead, J. L. (2012) · Applied Mathematics and Computation · doi:10.1016/j.amc.2012.11.067 · Cited by 11

Estimating the Largest Elements of a Matrix

Higham, N. J., & Relton, S. D. (2016) · SIAM Journal on Scientific Computing · doi:10.1137/15m1053645 · Cited by 11

Algorithms and perturbation theory for matrix eigenvalue problems and the singular value decomposition

Freund, R. W., & Nakatsukasa, Y. (2011) · Cited by 11

Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map

Araujo-Cabarcas, J. C., Engström, C., & Elias Jarlebring, A. (2017) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2017.08.012 · Cited by 11

Hypergeometric Functions: From One Scalar Variable to Several Matrix Arguments, in Statistics and Beyond

Pham-Gia, T., & Thanh, D. N. (2016) · Open Journal of Statistics · doi:10.4236/ojs.2016.65078 · Cited by 11

Computing the Wave-Kernel Matrix Functions

Nadukandi, P., & Higham, N. J. (2018) · SIAM Journal on Scientific Computing · doi:10.1137/18m1170352 · Cited by 11

NEP

Campos, C., & Román, J. E. (2021) · ACM Transactions on Mathematical Software · doi:10.1145/3447544 · Cited by 11

Backward Itô–Ventzell and stochastic interpolation formulae

Moral, P. D., & Singh, S. S. (2022) · Stochastic Processes and their Applications · doi:10.1016/j.spa.2022.09.007 · Cited by 11

System Aliasing in Dynamic Network Reconstruction:Issues on Low Sampling Frequencies

Yue, Z., Thunberg, J., Lennart Ljung, A., Yuan, Y., & Gonçalves, J. M. (2020) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2020.3042487 · Cited by 11

Matrix Arithmetic-Geometric Mean and the Computation of the Logarithm

Cardoso, J. R., & Ralha, R. (2016) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/140998226 · Cited by 11

Rational Krylov Methods for Nonlinear Eigenvalue Problems

Beeumen, R. V. (2013) · Cited by 11

Descriptor System Tools (DSTOOLS) User's GuidePreprint

Varga, A. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1707.07140 · Cited by 11

A posteriori error estimates of Krylov subspace approximations to matrix functionsPreprint

Jia, Z., & Lv, H. (2016) · Cited by 11

Core shrinkage covariance estimation for matrix-variate data

Hoff, P. D., McCormack, A., & Zhang, A. R. (2023) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1093/jrsssb/qkad070 · Cited by 10

Observer-Based Control for Linear Continuous-Time Systems With Fully Homomorphic Encryption

Nguyen, H., Bình, N. T., Lee, H.-G., & Ahn, H. (2024) · IEEE Transactions on Control of Network Systems · doi:10.1109/tcns.2024.3401268 · Cited by 10

Quantum and Classical Query Complexities of Functions of Matrices

Montanaro, A., & Shao, C. (2024) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/3618260.3649665 · Cited by 17

Subspace Representation Learning for Sparse Linear Arrays to Localize More Sources Than Sensors: A Deep Learning Methodology

Chen, K.-L., & Rao, B. D. (2025) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2025.3544170 · Cited by 10

Reduced ambiguity calibration for LOFAR

Yatawatta, S. (2012) · Experimental Astronomy · doi:10.1007/s10686-012-9300-7 · Cited by 10

Estimates for the generalized cross-validation function via an extrapolation and statistical approach

Mitrouli, M., & Roupa, P. (2018) · CALCOLO · doi:10.1007/s10092-018-0266-3 · Cited by 10

Fast, Asymptotically Efficient, Recursive Estimation in a Riemannian Manifold

Zhou, J., & Said, S. (2019) · Entropy · doi:10.3390/e21101021 · Cited by 10

A new method for online identification of civil structures: Virtual synchronization

Ghaderi, P., & Amini, F. (2018) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.2948 · Cited by 10

Stable Computation of Generalized Matrix Functions via Polynomial Interpolation

Aurentz, J. L., Austin, A. P., Michele Benzi, A., & Kalantzis, V. (2019) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/18m1191786 · Cited by 10

Multi‐layer distributed protocols for robust cooperative tracking in interconnected nonlinear multiagent systems

Rezaei, V., & Stefanovic, M. (2019) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.4579 · Cited by 10

A family of high order iterations for calculating the sign of a matrix

Soleymani, F., Khdhr, F. W., Saeed, R. K., & Golzarpoor, J. (2020) · Mathematical Methods in the Applied Sciences · doi:10.1002/mma.6471 · Cited by 10

Identification of Nonlinear Systems Using the Infinitesimal Generator of the Koopman Semigroup—A Numerical Implementation of the Mauroy–Goncalves Method

Drmač, Z., Mezić, I., & Mohr, R. (2021) · Mathematics · doi:10.3390/math9172075 · Cited by 10

Sensitivity of Matrix Function Based Network Communicability Measures: Computational Methods and A Priori Bounds

Schweitzer, M. (2023) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/23m1556708 · Cited by 10

Recursive quantum eigenvalue and singular-value transformation: Analytic construction of matrix sign function by Newton iteration

Mizuta, K., & Fujii, K. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.l012007 · Cited by 10

Speeding Up Krylov Subspace Methods for Computing \(\boldsymbol{{f}(A){b}}\) via Randomization

Cortinovis, A., Kreßner, D., & Nakatsukasa, Y. (2024) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/22m1543458 · Cited by 10

Efficient Solvers for Saddle Point Problems with Applications to PDE–Constrained Optimization

Zulehner, W. (2012) · Lecture notes in applied and computational mechanics · doi:10.1007/978-3-642-30316-6_9 · Cited by 10

Survey on the Technique of Hierarchical Matrices

Hackbusch, W. (2015) · Vietnam Journal of Mathematics · doi:10.1007/s10013-015-0168-5 · Cited by 10

Power-Law Noises over General Spatial Domains and on Nonstandard Meshes

van Wyk, H., Gunzburger, M., Burkhardt, J., & Stoyanov, M. (2015) · SIAM/ASA Journal on Uncertainty Quantification · doi:10.1137/140985433 · Cited by 10

Characterizations of matrix and operator-valued Φ-entropies, and operator Efron–Stein inequalities

Cheng, H.-C., & Hsieh, M.-H. (2016) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2015.0563 · Cited by 10

Continuum limits of matrix product states

Cuevas, G. D. L., Schuch, N., Pérez-Garcı́a, D., & Cirac, J. I. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.98.174303 · Cited by 10

О функциях от квазитeплицевых матриц

Bini, D. A., Massei, S., & Meini, B. (2017) · Математический сборник · doi:10.4213/sm8864 · Cited by 10

Optimal Bayesian design for model discrimination via classification

Hainy, M., Price, D. J., Restif, O., & Drovandi, C. (2022) · Statistics and Computing · doi:10.1007/s11222-022-10078-2 · Cited by 10

Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment

Zern, A., Zisler, M., Petra, S., & Schnörr, C. (2019) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-019-00935-7 · Cited by 10

On an improved computational solution for the 3D HCIR PDE in finance

Soleymani, F., Akgül, A., & Akgül, E. K. (2019) · Analele Universităţii "Ovidius" Constanţa. Seria Matematică · doi:10.2478/auom-2019-0042 · Cited by 10

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

Shi, L., & Chi, Y. (2020) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp40776.2020.9054356 · Cited by 10

A Fast and Accurate Accelerometer and Magnetometer Alignment Algorithm

Papafotis, K., & Sotiriadis, P. P. (2020) · IEEE Sensors Journal · doi:10.1109/jsen.2020.3011579 · Cited by 10

Kolmogorov-Arnold-Moser Stability for Conserved Quantities in Finite-Dimensional Quantum Systems

Burgarth, D. K., Paolo Facchi, A., Nakazato, H., Pascazio, S., & Yuasa, K. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.150401 · Cited by 10

Efficient exponential time integration for simulating nonlinear coupled oscillators

Luân, V. T., & Michels, D. L. (2021) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2021.113429 · Cited by 10

A Multilevel Approach to Variance Reduction in the Stochastic Estimation of the Trace of a Matrix

Frommer, A., Khalil, M. N., & Ramirez‐Hidalgo, G. (2022) · SIAM Journal on Scientific Computing · doi:10.1137/21m1441894 · Cited by 10

Finite Torsion of Compressible Circular Cylinders: An Approximate Solution

Falope, F. O., Lanzoni, L., & Tarantino, A. M. (2022) · Journal of Elasticity · doi:10.1007/s10659-022-09928-x · Cited by 10

Laplacian Filtered Loop-Star Decompositions and Quasi-Helmholtz Filters: Definitions, Analysis, and Efficient Algorithms

Merlini, A., Henry, C., Consoli, D., Rahmouni, L., Dély, A., & Andriulli, F. P. (2023) · IEEE Transactions on Antennas and Propagation · doi:10.1109/tap.2023.3283043 · Cited by 10

Bridging the Performance Gap Between Two-Way and One-Way CSI-Based 5 GHz WiFi Ranging

Helwa, S., Marter, J. P. V., Shoudha, S. N., Ben-Shachar, M., Alpert, Y., Dabak, A. G., Torlak, M., & Al‐Dhahir, N. (2023) · IEEE Access · doi:10.1109/access.2023.3287850 · Cited by 10

Strong Migration Limit for Games in Structured Populations: Applications to Dominance Hierarchy and Set Structure

Kroumi, D., & Lessard, S. (2015) · Games · doi:10.3390/g6030318 · Cited by 10

On explicit formulas for the principal matrix logarithm

Marrero, J. A., Taher, R. B., & Rachidi, M. (2013) · Applied Mathematics and Computation · doi:10.1016/j.amc.2013.06.005 · Cited by 10

Sequential Monte Carlo EM for multivariate probit models

Moffa, G., & Kuipers, J. (2013) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2013.10.019 · Cited by 10

The structure of matrices in rational Gauss quadrature

Jagels, C., & Lothar Reichel, B. (2013) · Mathematics of Computation · doi:10.1090/s0025-5718-2013-02695-6 · Cited by 10

Exponential Quadrature Rules for Linear Fractional Differential Equations

Garrappa, R., & Popolizio, M. (2014) · Mediterranean Journal of Mathematics · doi:10.1007/s00009-014-0396-z · Cited by 10

Methods for verified stabilizing solutions to continuous-time algebraic Riccati equations

Haqiri, T., & Poloni, F. (2016) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2016.09.021 · Cited by 10

On the Hermite--Hadamard inequality for convex functions of two variables

Lyu, S. (2013) · Numerical Algebra Control and Optimization · doi:10.3934/naco.2014.4.1 · Cited by 10

Auto-regressive moving-average discrete-time dynamical systems and autocorrelation functions on real-valued Riemannian matrix manifolds

Fiori, S. (2014) · Discrete and Continuous Dynamical Systems - B · doi:10.3934/dcdsb.2014.19.2785 · Cited by 10

Gauss quadrature for quasi-definite linear functionals

Pozza, S., Pranić, M. S., & Strakoš, Z. (2016) · IMA Journal of Numerical Analysis · doi:10.1093/imanum/drw032 · Cited by 10

Exploring the “Middle Earth” of network spectra via a Gaussian matrix function

Estrada, E., Alhomaidhi, A. A., & Al-Thukair, F. A. (2017) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4976015 · Cited by 11

Analysis of inexact Krylov subspace methods for approximating the matrix exponential

Dinh, K. N., & Sidje, R. B. (2017) · Mathematics and Computers in Simulation · doi:10.1016/j.matcom.2017.01.002 · Cited by 10

A Truncated Taylor Series Algorithm for Computing the Action of Trigonometric and Hyperbolic Matrix Functions

Al-Mohy, A. H. (2018) · SIAM Journal on Scientific Computing · doi:10.1137/17m1145227 · Cited by 10

Backward error analysis of polynomial approximations for computing the action of the matrix exponential

Marco Caliari, A., Kandolf, P., & Zivcovich, F. (2018) · BIT Numerical Mathematics · doi:10.1007/s10543-018-0718-9 · Cited by 10

Parametric randomization, complex symplectic factorizations, and quadratic-exponential functionals for Gaussian quantum states

Vladimirov, I. G., Petersen, I. R., & James, M. R. (2019) · Infinite Dimensional Analysis Quantum Probability and Related Topics · doi:10.1142/s0219025719500206 · Cited by 10

The smallest eigenvalue of large Hankel matrices

Zhu, M., Chen, Y., Emmart, N., & Weems, C. (2018) · Applied Mathematics and Computation · doi:10.1016/j.amc.2018.04.012 · Cited by 10

Computation of Green’s Function of the Bounded Solutions Problem

Kurbatov, V. G., & Курбатова, И. В. (2017) · Computational Methods in Applied Mathematics · doi:10.1515/cmam-2017-0042 · Cited by 10

Network Autocorrelation Modeling: Bayesian Techniques for Estimating and Testing Multiple Network Autocorrelations

Dittrich, D., Leenders, R., & Mulder, J. (2020) · Sociological Methodology · doi:10.1177/0081175020913899 · Cited by 10

Qualitative chirality effects on the Casimir-Lifshitz torque with liquid crystals

Broer, W., Lu, B.-S., & Podgornik, R. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.033238 · Cited by 10

Fisher Vector Coding for Covariance Matrix Descriptors Based on the Log-Euclidean and Affine Invariant Riemannian Metrics

Ilea, I., Bombrun, L., Said, S., & Berthoumieu, Y. (2018) · Journal of Imaging · doi:10.3390/jimaging4070085 · Cited by 10

Degrees of freedom for nonlinear least squares estimationPreprint

Hansen, N. R., & Sokol, A. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1402.2997 · Cited by 10

Roots of Stochastic Matrices and Fractional Matrix Powers

Lijing Lin, A. (2011) · MIMS EPrints (University of Southampton) · Cited by 10

Convex Optimization with Random Pursuit

Stich, S. U. (2014) · Repository for Publications and Research Data (ETH Zurich) · doi:10.3929/ethz-a-010377352 · Cited by 10

An efficient implementation of an implicit FEM scheme for fractional-in-space reaction-diffusion equations

Burrage, K., Hale, N., & Kay, D. (2011) · Oxford University Research Archive (ORA) (University of Oxford) · Cited by 10

Algebraic Varieties in Quantum Chemistry

Faulstich, F. M., Sturmfels, B., & Sverrisdóttir, S. (2024) · Foundations of Computational Mathematics · doi:10.1007/s10208-024-09657-8 · Cited by 9

A Concise Parametrization of Affine Transformation

Kaji, S., & Ochiai, H. (2016) · SIAM Journal on Imaging Sciences · doi:10.1137/16m1056936 · Cited by 9

fenics_ice 1.0: a framework for quantifying initialization uncertainty for time-dependent ice sheet models

Koziol, C. P., Todd, J., Goldberg, D., & Maddison, J. R. (2021) · Geoscientific model development · doi:10.5194/gmd-14-5843-2021 · Cited by 9

On the intrinsic structure of the solution set to the Yang–Baxter-like matrix equation

Dinčić, N. Č., & Djordjević, B. D. (2022) · Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas · doi:10.1007/s13398-022-01214-8 · Cited by 9

Riemannian Geometric-Nonlinear Conjugate Gradient Model Order Reduction of Linear Port-Hamiltonian Systems on Finite Frequency Intervals

Xu, K.-L., & Jiang, Y. (2023) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2023.3321902 · Cited by 9

On generating Sobolev orthogonal polynomials

Buggenhout, N. V. (2023) · Numerische Mathematik · doi:10.1007/s00211-023-01379-3 · Cited by 9

Edge importance in complex networks

Noschese, S., & Lothar Reichel, B. (2024) · Numerical Algorithms · doi:10.1007/s11075-024-01881-1 · Cited by 9

Nonparametric two-sample hypothesis testing for low-rank random graphs of differing sizes

Agterberg, J., Tang, M., & Priebe, C. (2026) · Electronic Journal of Statistics · doi:10.1214/26-ejs2508 · Cited by 9

Computing the maximum amplification of the solution norm of differential-algebraic systems

Бойко, А. В., Nechepurenko, Y. M., & Sadkane, M. (2012) · Computational Mathematics and Modeling · doi:10.1007/s10598-012-9132-3 · Cited by 9

Evaluating and Approximating FIR Filters: An Approach Based on Functions of Matrices

Michiels, W., & Ünal, H. U. (2014) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2014.2326295 · Cited by 9

Structured Matrix Nearness Problems:Theory and Algorithms

Borsdorf, R. (2012) · Cited by 9

Parallel Direct Solution of the Ensemble Square Root Kalman Filter Equations with Observation Principal Components

Steward, J., Aksoy, A., & Haddad, Z. S. (2017) · Journal of Atmospheric and Oceanic Technology · doi:10.1175/jtech-d-16-0140.1 · Cited by 9

Linear Combination of Independent Exponential Random Variables

Li, K.-H., & Li, C. T. (2018) · Methodology And Computing In Applied Probability · doi:10.1007/s11009-018-9653-0 · Cited by 9

Global Gated Mixture of Second-order Pooling for Improving Deep Convolutional Neural Networks

Wang, Q., Gao, Z., Xie, J., Zuo, W., & Li, P. (2018) · neural information processing systems · Cited by 9

Verified computation for the matrix principal logarithm

Miyajima, S. (2019) · Linear Algebra and its Applications · doi:10.1016/j.laa.2019.01.008 · Cited by 9

Means and covariances of photon numbers in multimode Gaussian states

Vallone, G., Cariolaro, G., & Pierobon, G. L. (2019) · Physical Review A · doi:10.1103/physreva.99.023817 · Cited by 9

Verification Methodology for Discrete Event Simulation Models of Personnel in the Canadian Armed Forces

Henderson, J. A., & Bryce, R. M. (2019) · Winter Simulation Conference · doi:10.1109/wsc40007.2019.9004841 · Cited by 9

Approximate tensor decompositions: Disappearance of many separations

Cuevas, G. D. L., Klingler, A., & Netzer, T. (2021) · Journal of Mathematical Physics · doi:10.1063/5.0033876 · Cited by 9

Verified computation of matrix gamma function

Miyajima, S. (2020) · Linear and Multilinear Algebra · doi:10.1080/03081087.2020.1757602 · Cited by 9

Continuous scaled phase-type distributions

Albrecher, H., Bladt, M., Bladt, M., & Yslas, J. (2022) · Stochastic Models · doi:10.1080/15326349.2022.2089683 · Cited by 9

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