Functions of Matrices: Theory and Computation

Superior performance of using hyperbolic sine activation functions in ZNN illustrated via time-varying matrix square roots finding

Zhang, Y., Jin, L., & Ke, Z. (2012) · Computer Science and Information Systems · doi:10.2298/csis120121043z · Cited by 30

Some notes on properties of the matrix Mittag-Leffler function

Sadeghi, A., & Cardoso, J. R. (2018) · Applied Mathematics and Computation · doi:10.1016/j.amc.2018.06.037 · Cited by 30

Efficient Low-Rank Solution of Large-Scale Matrix Equations

Kürschner, P. (2016) · MPG.PuRe (Max Planck Society) · Cited by 30

ON THE DISPERSION AND SCATTERING OF MAGNETOHYDRODYNAMIC WAVES BY LONGITUDINALLY STRATIFIED FLUX TUBES

Andries, J., & Cally, P. S. (2011) · The Astrophysical Journal · doi:10.1088/0004-637x/743/2/164 · Cited by 29

A Koopman-based residual modeling approach for the control of a soft robot arm

Bruder, D. M., Bombara, D. J., & Wood, R. J. (2024) · The International Journal of Robotics Research · doi:10.1177/02783649241272114 · Cited by 29

Numerically stable improved Chebyshev–Halley type schemes for matrix sign function

Cordero, A., Soleymani, F., Torregrosa, J. R., & Ullah, M. Z. (2016) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2016.10.025 · Cited by 29

Low-complexity 8-point DCT approximation based on angle similarity for image and video coding

Oliveira, R. S., Cintra, R. J., Bayer, F. M., da Silveira, T. L. T., Madanayake, A., & Leite, A. (2018) · Multidimensional Systems and Signal Processing · doi:10.1007/s11045-018-0601-5 · Cited by 29

Discrete Symbol Calculus

Demanet, L., & Ying, L. (2011) · SIAM Review · doi:10.1137/080731311 · Cited by 29

High performance computing of the matrix exponential

Ruiz, P. A., Sastre, J., Ibáñez, J., & Defez, E. (2015) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2015.04.001 · Cited by 29

Semi-global Kuranishi charts and the definition of contact homology

Bao, E., & Honda, K. (2023) · Advances in Mathematics · doi:10.1016/j.aim.2023.108864 · Cited by 29

A fast convergent numerical method for matrix sign function with application in SDEs

Soheili, A. R., Toutounian, F., & Soleymani, F. (2015) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2014.12.041 · Cited by 28

A stiffly accurate integrator for elastodynamic problems

Michels, D. L., Luân, V. T., & Tokman, M. (2017) · ACM Transactions on Graphics · doi:10.1145/3072959.3073706 · Cited by 28

XT race : Making the Most of Every Sample in Stochastic Trace Estimation

Epperly, E. N., Tropp, J. A., & Webber, R. J. (2024) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/23m1548323 · Cited by 28

Context-aware personalized program guide based on neural network

Krstić, M., & Bjelica, M. (2012) · IEEE Transactions on Consumer Electronics · doi:10.1109/tce.2012.6414999 · Cited by 28

Superlinear convergence of the rational Arnoldi method for the approximation of matrix functions

Beckermann, B., & Güttel, S. (2012) · Numerische Mathematik · doi:10.1007/s00211-011-0434-8 · Cited by 28

Hyperspherical embedding of graphs and networks in communicability spaces

Estrada, E., Sánchez-Lirola, M. G., & de la Peña, J. A. (2013) · Discrete Applied Mathematics · doi:10.1016/j.dam.2013.05.032 · Cited by 28

Efficient orthogonal matrix polynomial based method for computing matrix exponential

Sastre, J., Ibáñez, J., Defez, E., & Ruiz, P. A. (2011) · Applied Mathematics and Computation · doi:10.1016/j.amc.2011.01.004 · Cited by 28

Computing the exponential of large block-triangular block-Toeplitz matrices encountered in fluid queues

Bini, D. A., Dendievel, S., Latouche, G., & Meini, B. (2015) · Linear Algebra and its Applications · doi:10.1016/j.laa.2015.03.035 · Cited by 27

Hermitian matrix polynomials with real eigenvalues of definite type. Part I: Classification

Alammari, M., & Françoise Tisseur, B. (2010) · Linear Algebra and its Applications · doi:10.1016/j.laa.2010.08.035 · Cited by 27

Solving the time-varying tensor square root equation by varying-parameters finite-time Zhang neural network

Mo, C., Gerontitis, D. K., & Stanimirović, P. S. (2021) · Neurocomputing · doi:10.1016/j.neucom.2021.03.011 · Cited by 27

Generalization of the Multiplicative and Additive Compounds of Square Matrices and Contraction Theory in the Hausdorff Dimension

Wu, C., Pines, R., Michael Margaliot, A., & Slotine, J.-J. E. (2022) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2022.3162547 · Cited by 27

Finite-time optimal formation control of multi-agent systems on the Lie group SE(3)

Liu, Y., & Geng, Z. (2013) · International Journal of Control · doi:10.1080/00207179.2013.792006 · Cited by 27

A Low-Rank Approximation for Computing the Matrix Exponential Norm

Nechepurenko, Y. M., & Sadkane, M. (2011) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/100789774 · Cited by 27

Geometric mean of bimetric spacetimes

Kocic, M. (2021) · Classical and Quantum Gravity · doi:10.1088/1361-6382/abdf28 · Cited by 28

Linear Credit Risk Models

Ackerer, D., & Filipović, D. (2016) · Finance and Stochastics · doi:10.1007/s00780-019-00409-z · Cited by 27

Scalable $M$-Channel Critically Sampled Filter Banks for Graph Signals

Li, S., Jin, Y., & Shuman, D. I. (2019) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2019.2923142 · Cited by 27

Frequency- and time-limited balanced truncation for large-scale second-order systems

Benner, P., & Werner, S. W. R. (2020) · Linear Algebra and its Applications · doi:10.1016/j.laa.2020.06.024 · Cited by 27

The Forest Consensus Theorem

Chebotarev, P., & Пашаевич, А. Р. (2014) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2014.2304369 · Cited by 27

Network DeconvolutionPreprint

Ye, C., Evanusa, M., He, H. W., Mitrokhin, A., Goldstein, T., Yorke, J. A., Fermuller, C. M., & Aloimonos, Y. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1905.11926 · Cited by 27

A Generalized Nyquist-Shannon Sampling Theorem Using the Koopman Operator

Zeng, Z., Liu, J., & Yuan, Y. (2024) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2024.3436610 · Cited by 26

Matching exponential-based and resolvent-based centrality measures

Aprahamian, M., Higham, D. J., & Higham, N. J. (2015) · Journal of Complex Networks · doi:10.1093/comnet/cnv016 · Cited by 26

Geometric numerical integration of the assignment flow

Zeilmann, A., Savarino, F., Petra, S., & Schnörr, C. (2019) · Inverse Problems · doi:10.1088/1361-6420/ab2772 · Cited by 26

Fitting inhomogeneous phase‐type distributions to data: the univariate and the multivariate case

Albrecher, H., Bladt, M., & Yslas, J. (2020) · Scandinavian Journal of Statistics · doi:10.1111/sjos.12505 · Cited by 26

A Dimensional Splitting Exponential Time Differencing Scheme for Multidimensional Fractional Allen-Cahn Equations

Chen, H., & Sun, H. (2021) · Journal of Scientific Computing · doi:10.1007/s10915-021-01431-0 · Cited by 26

Mittag--Leffler Functions and their Applications in Network Science

Arrigo, F., & Durastante, F. (2021) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/21m1407276 · Cited by 26

Redundancy-aware Electromigration checking for mesh power grids

Chatterjee, S., Fawaz, M., & Najm, F. N. (2013) · International Conference on Computer Aided Design · doi:10.1109/iccad.2013.6691168 · Cited by 26

Entanglement classes of permutation-symmetric qudit states: Symmetric operations suffice

Migdał, P., Rodríguez-Laguna, J., & Lewenstein, M. (2013) · Physical Review A · doi:10.1103/physreva.88.012335 · Cited by 28

A pseudo-spectral scheme for the approximate solution of a time-fractional diffusion equation

Esmaeili, S., & Garrappa, R. (2014) · International Journal of Computer Mathematics · doi:10.1080/00207160.2014.915962 · Cited by 26

A modified Casteljau algorithm to solve interpolation problems on Stiefel manifolds

Krakowski, K., Machado, L., Leite, F. S., & Batista, J. P. (2016) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2016.07.018 · Cited by 26

A comparison of reduced and unreduced KKT systems arising from interior point methods

Morini, B., Simoncini, V., & Tani, M. (2017) · Computational Optimization and Applications · doi:10.1007/s10589-017-9907-8 · Cited by 26

Efficient evaluation of matrix polynomials

Sastre, J. (2017) · Linear Algebra and its Applications · doi:10.1016/j.laa.2017.11.010 · Cited by 26

Asymptotic gap probability distributions of the Gaussian unitary ensembles and Jacobi unitary ensembles

Lyu, S., Chen, Y., & Fan, E. (2017) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2017.11.018 · Cited by 26

Improving the Accuracy of the Chebyshev Rational Approximation Method Using Substeps

Isotalo, A., & Pusa, M. (2016) · Nuclear Science and Engineering · doi:10.13182/nse15-67 · Cited by 25

Semi-analytical solution for time-fractional diffusion equation based on finite difference method of lines (MOL)

Kazem, S., & Dehghan, M. (2018) · Engineering With Computers · doi:10.1007/s00366-018-0595-5 · Cited by 25

Algebraic Neural Networks: Stability to Deformations

Parada-Mayorga, A., & Ribeiro, A. (2021) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2021.3084537 · Cited by 25

RBF-FD solution for a financial partial-integro differential equation utilizing the generalized multiquadric function

Soleymani, F., & Zhu, S. (2020) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2020.11.010 · Cited by 25

Fast computation of matrix function-based centrality measures for layer-coupled multiplex networks

Bergermann, K., & Stoll, M. (2022) · Physical review. E · doi:10.1103/physreve.105.034305 · Cited by 30

Interior Eigenvalues from Density Matrix Expansions in Quantum Mechanical Molecular Dynamics

Rubensson, E. H., & Niklasson, A. M. N. (2014) · SIAM Journal on Scientific Computing · doi:10.1137/130911585 · Cited by 25

Reorthogonalization for the Golub–Kahan–Lanczos bidiagonal reduction

Barlow, J. L. (2013) · Numerische Mathematik · doi:10.1007/s00211-013-0518-8 · Cited by 25

Automatic Generation of Fast and Certified Code for Polynomial Evaluation

Mouilleron, C., & Revy, G. (2011) · IEEE Symposium on Computer Arithmetic (ARITH) · doi:10.1109/arith.2011.39 · Cited by 25

Backward Stability of Iterations for Computing the Polar Decomposition

Nakatsukasa, Y., & Higham, N. J. (2012) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/110857544 · Cited by 25

Inexact implementation using Krylov subspace methods for large scale exponential discriminant analysis with applications to high dimensionality reduction problems

Wu, G., Feng, T., Zhang, L., & Yang, M. (2016) · Pattern Recognition · doi:10.1016/j.patcog.2016.08.020 · Cited by 25

Multiprecision Algorithms for Computing the Matrix Logarithm

Fasi, M., & Higham, N. J. (2018) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/17m1129866 · Cited by 25

Preparation of Hadamard Gate for Open Quantum Systems by the Lyapunov Control Method

Ghaeminezhad, N., & Cong, S. (2018) · IEEE/CAA Journal of Automatica Sinica · doi:10.1109/jas.2018.7511084 · Cited by 25

Boosting the computation of the matrix exponential

Sastre, J., Ibáñez, J., & Defez, E. (2018) · Applied Mathematics and Computation · doi:10.1016/j.amc.2018.08.017 · Cited by 25

Graph Fractional Fourier Transform: A Unified Theory

Alikaşifoğlu, T., Kartal, B., & Koç, A. (2024) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2024.3439211 · Cited by 27

Accounting for the role of long walks on networks via a new matrix function

Estrada, E., & Silver, G. (2017) · Journal of Mathematical Analysis and Applications · doi:10.1016/j.jmaa.2016.12.062 · Cited by 24

Evaluation of the quasi correlated tight-binding (QCTB) model for describing polyradical character in polycyclic hydrocarbons

Luzanov, A. V., Plasser, F., Das, A., & Lischka, H. (2017) · The Journal of Chemical Physics · doi:10.1063/1.4975196 · Cited by 24

On commuting solutions of the Yang–Baxter-like matrix equation

Shen, D., Wei, M., & Jia, Z. (2018) · Journal of Mathematical Analysis and Applications · doi:10.1016/j.jmaa.2018.02.030 · Cited by 24

Improved Variants of the Hutch++ Algorithm for Trace Estimation

Persson, D., Cortinovis, A., & Kreßner, D. (2022) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/21m1447623 · Cited by 24

Two Optimal General Classes of Iterative Methods with Eighth-Order

Cordero, A., Lotfi, T., Mahdiani, K., & Torregrosa, J. R. (2014) · Acta Applicandae Mathematicae · doi:10.1007/s10440-014-9869-0 · Cited by 24

Exploiting the monthly data flow in structural forecasting

Giannone, D., Monti, F., & Reichlin, L. (2016) · Journal of Monetary Economics · doi:10.1016/j.jmoneco.2016.10.011 · Cited by 24

Homogenization of long fiber reinforced composites including fiber bending effects

Poulios, K., & Niordson, C. F. (2016) · Journal of the Mechanics and Physics of Solids · doi:10.1016/j.jmps.2016.04.010 · Cited by 24

Beyond spatial scalability limitations with a massively parallel method for linear oscillatory problems

Schreiber, M., Peixoto, P. S., Haut, T. S., & Wingate, B. (2017) · The International Journal of High Performance Computing Applications · doi:10.1177/1094342016687625 · Cited by 24

Numerical Solution of Time-Dependent Problems with Fractional Power Elliptic Operator

Vabishchevich, P. N. (2017) · Computational Methods in Applied Mathematics · doi:10.1515/cmam-2017-0028 · Cited by 24

Theoretical Analysis of Groundwater Flow Patterns Near Stagnation Points

Bresciani, É., Kang, P. K., & Lee, S. (2019) · Water Resources Research · doi:10.1029/2018wr023508 · Cited by 24

Pseudospectral Shattering, the Sign Function, and Diagonalization in Nearly Matrix Multiplication Time

Banks, J., Garza-Vargas, J., Kulkarni, A., & Srivastava, N. (2022) · Foundations of Computational Mathematics · doi:10.1007/s10208-022-09577-5 · Cited by 31

A Second-Order, Linear, \(\boldsymbol{L^\infty}\)-Convergent, and Energy Stable Scheme for the Phase Field Crystal Equation

Li, X., & Qiao, Z. (2024) · SIAM Journal on Scientific Computing · doi:10.1137/23m1552164 · Cited by 23

Bimetric gravity improves the fit to DESI BAO and eases the Hubble tension

Högås, M., & Mörtsell, E. (2025) · Physical review. D/Physical review. D. · doi:10.1103/zz5k-kzzk · Cited by 23

A Regularization Framework for Learning Over Multitask Graphs

Nassif, R., Vlaski, S., Richard, C., & Sayed, A. H. (2018) · IEEE Signal Processing Letters · doi:10.1109/lsp.2018.2889267 · Cited by 23

An Algorithm for Improving Non-Local Means Operators via Low-Rank Approximation

May, V., Keller, Y., Sharon, N., & Shkolnisky, Y. (2016) · IEEE Transactions on Image Processing · doi:10.1109/tip.2016.2518805 · Cited by 23

Exponential Martingales and Changes of Measure for Counting Processes

Sokol, A., & Hansen, N. R. (2015) · Stochastic Analysis and Applications · doi:10.1080/07362994.2015.1040890 · Cited by 23

Sensitivity and Conditioning of the Truncated Total Least Squares Solution

Gratton, S., Titley-Péloquin, D., & Tshimanga, J. (2013) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/120895019 · Cited by 23

Point Cloud Glue: constraining simulations using the procrustes transform

Twigg, C. D., & Kačić-Alesić, Z. (2010) · doi:10.5555/1921427.1921435 · Cited by 23

Geometric means of structured matrices

Bini, D. A., Iannazzo, B., Jeuris, B., & Vandebril, R. (2013) · BIT Numerical Mathematics · doi:10.1007/s10543-013-0450-4 · Cited by 23

A Schur Logarithmic Algorithm for Fractional Powers of Matrices

Iannazzo, B., & Manasse, C. (2013) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/120877398 · Cited by 23

Polynomial algebra for Birkhoff interpolants

Butcher, J. C., Corless, R. M., González-Vega, L., & Shakoori, A. (2010) · Numerical Algorithms · doi:10.1007/s11075-010-9385-x · Cited by 23

Rediscovering GF Becker’s early axiomatic deduction of a multiaxial nonlinear stress–strain relation based on logarithmic strain

Neff, P., Münch, I., & Martin, R. J. (2014) · Mathematics and Mechanics of Solids · doi:10.1177/1081286514542296 · Cited by 23

The restarted shift-and-invert Krylov method for matrix functions

Moret, I., & Popolizio, M. (2012) · Numerical Linear Algebra with Applications · doi:10.1002/nla.1862 · Cited by 23

Complex martingales and asymptotic enumeration

Isaev, M., & McKay, B. D. (2017) · Random Structures and Algorithms · doi:10.1002/rsa.20754 · Cited by 23

Low-Rank Updates of Matrix Functions

Beckermann, B., Kreßner, D., & Schweitzer, M. (2018) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/17m1140108 · Cited by 23

Exponential methods for solving hyperbolic problems with application to collisionless kinetic equations

Crouseilles, N., Einkemmer, L. D., & Massot, J. (2020) · Journal of Computational Physics · doi:10.1016/j.jcp.2020.109688 · Cited by 23

Frequency-Limited Reduced Models for Linear and Bilinear Systems on the Riemannian Manifold

Jiang, Y., & Xu, K.-L. (2020) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2020.3027643 · Cited by 23

Mixed Frequency Structural Vector Auto-Regressive Models

Foroni, C., & Marcellino, M. G. (2015) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/rssa.12120 · Cited by 23

A family of Adams exponential integrators for fractional linear systems

Garrappa, R. (2013) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2013.01.022 · Cited by 23

Genetic Distance for a General Non-Stationary Markov Substitution Process

Kaehler, B. D., Yap, V. B., Zhang, R., & Huttley, G. A. (2014) · Systematic Biology · doi:10.1093/sysbio/syu106 · Cited by 23

A perturbation analysis of stochastic matrix Riccati diffusions

Bishop, A. N., Moral, P. D., & Niclas, A. (2020) · Annales de l Institut Henri Poincaré Probabilités et Statistiques · doi:10.1214/19-aihp987 · Cited by 23

Spectrum Approximation Beyond Fast Matrix Multiplication: Algorithms and HardnessPreprint

Musco, C., Netrapalli, P., Sidford, A., Ubaru, S., & Woodruff, D. P. (2017) · arXiv (Cornell University) · doi:10.4230/lipics.itcs.2018.8 · Cited by 23

A Formula for the Fréchet Derivative of a Generalized Matrix Function

Noferini, V. (2017) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/16m1072851 · Cited by 22

Model reduction techniques for the computation of extended Markov parameterizations for generalized Langevin equations

Bockius, N., Shea, J., Jung, G., Schmid, F., & Hanke, M. (2021) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/abe6df · Cited by 22

Approximating the Matrix Sign Function Using a Novel Iterative Method

Soleymani, F., Stanimirović, P. S., Shateyi, S., & Haghani, F. K. (2014) · Abstract and Applied Analysis · doi:10.1155/2014/105301 · Cited by 22

From empirical data to time-inhomogeneous continuous Markov processes

Lencastre, P., Raischel, F., Rogers, T., & Lind, P. G. (2016) · Physical review. E · doi:10.1103/physreve.93.032135 · Cited by 22

Dynamics of theN-link pendulum: a fractional perspective

Lopes, A. M., & Machado, J. A. T. (2015) · International Journal of Control · doi:10.1080/00207179.2015.1126677 · Cited by 22

Quasi-Toeplitz matrix arithmetic: a MATLAB toolbox

Bini, D. A., Massei, S., & Robol, L. (2018) · Numerical Algorithms · doi:10.1007/s11075-018-0571-6 · Cited by 22

A literature survey of matrix methods for data science

Stoll, M. (2020) · GAMM-Mitteilungen · doi:10.1002/gamm.202000013 · Cited by 25

General Conditions to Realize Exceptional Points of Degeneracy in Two Uniform Coupled Transmission Lines

Mealy, T., & Capolino, F. (2020) · IEEE Transactions on Microwave Theory and Techniques · doi:10.1109/tmtt.2020.2999498 · Cited by 22

On modeling of plasmonic devices: overview

Said, A. M. A., Atia, K. S. R., & Obayya, S. S. A. (2020) · Journal of the Optical Society of America B · doi:10.1364/josab.399121 · Cited by 22

Accurate matrix exponential computation to solve coupled differential models in engineering

Sastre, J., Ibáñez, J., Defez, E., & Ruiz, P. A. (2011) · Mathematical and Computer Modelling · doi:10.1016/j.mcm.2010.12.049 · Cited by 22

Distributed Control in Multiple Dimensions: A Structure Preserving Computational Technique

Rice, J. K., & Verhaegen, M. (2010) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2010.2063230 · Cited by 22

Graph Ranking Guarantees for Numerical Approximations to Katz Centrality

Nathan, E., Sanders, G., Fairbanks, J., Henson, V. E., & Bader, D. A. (2017) · Procedia Computer Science · doi:10.1016/j.procs.2017.05.021 · Cited by 22

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