Functions of Matrices: Theory and Computation

Scabies in residential care homes: Modelling, inference and interventions for well-connected population sub-units

Kinyanjui, T., Middleton, J., Güttel, S., Cassell, J., Ross, J. V., & House, T. (2018) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1006046 · Cited by 22

Two direct factorization methods for inverse scattering problems

Leem, K. H., Liu, J., & Pelekanos, G. (2018) · Inverse Problems · doi:10.1088/1361-6420/aae15e · Cited by 21

A Riemannian metric for geometry-aware singularity avoidance by articulated robots

Marić, F., Petrović, L., Guberina, M., Kelly, J. W., & Petrovic, I. K. (2021) · Robotics and Autonomous Systems · doi:10.1016/j.robot.2021.103865 · Cited by 21

Efficient computation of the matrix cosine

Sastre, J., Ibáñez, J., Ruiz, P. A., & Defez, E. (2013) · Applied Mathematics and Computation · doi:10.1016/j.amc.2013.01.043 · Cited by 21

GMRES Convergence for Perturbed Coefficient Matrices, with Application to Approximate Deflation Preconditioning

Sifuentes, J., Embree, M., & Morgan, R. B. (2013) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/120884328 · Cited by 21

Optical Axes of Eyes and Other Optical Systems

Harris, W. F. (2009) · Optometry and Vision Science · doi:10.1097/opx.0b013e31819fa8d8 · Cited by 21

Polar decomposition of oblique projections

Gustavo Corach, A., & Maestripieri, A. (2010) · Linear Algebra and its Applications · doi:10.1016/j.laa.2010.03.016 · Cited by 21

A stabilization algorithm of the Navier–Stokes equations based on algebraic Bernoulli equation

Amodei, L., & Buchot, J.-M. (2011) · Numerical Linear Algebra with Applications · doi:10.1002/nla.799 · Cited by 21

Applications of Trace Estimation Techniques

Ubaru, S., & Saad, Y. (2018) · Lecture notes in computer science · doi:10.1007/978-3-319-97136-0_2 · Cited by 21

Perturbative expansions of the conformation tensor in viscoelastic flows

Hameduddin, I., Gayme, D. F., & Zaki, T. A. (2018) · Journal of Fluid Mechanics · doi:10.1017/jfm.2018.777 · Cited by 21

The Hankel determinant associated with a singularly perturbed Laguerre unitary ensemble

Lyu, S., Griffin, J., & Chen, Y. (2018) · Journal of Nonlinear Mathematical Physics · doi:10.1080/14029251.2019.1544786 · Cited by 21

ON THE STATIONARITY OF DYNAMIC CONDITIONAL CORRELATION MODELS

Fermanian, J., & Malongo, H. (2016) · Econometric Theory · doi:10.1017/s0266466616000116 · Cited by 21

Numerical Solution of Nonstationary Problems for a Space-Fractional Diffusion Equation

Vabishchevich, P. N. (2016) · Fractional Calculus and Applied Analysis · doi:10.1515/fca-2016-0007 · Cited by 21

Constraints on bimetric gravity. Part I. Analytical constraints

Högås, M., & Mörtsell, E. (2021) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2021/05/001 · Cited by 21

Second-order encoding networks for semantic segmentation

Sun, Q., Zhang, Z., & Li, P. (2021) · Neurocomputing · doi:10.1016/j.neucom.2021.03.003 · Cited by 21

Multi-Scale Graph Convolutional Network With Spectral Graph Wavelet Frame

Shen, Y., Dai, W., Li, C., Zou, J., & Xiong, H. (2021) · IEEE Transactions on Signal and Information Processing over Networks · doi:10.1109/tsipn.2021.3109820 · Cited by 22

Fractional-hyperbolic systems

Kochubei, A. N. (2013) · Fractional Calculus and Applied Analysis · doi:10.2478/s13540-013-0053-4 · Cited by 21

Absolute and relative Weyl theorems for generalized eigenvalue problems

Nakatsukasa, Y. (2009) · Linear Algebra and its Applications · doi:10.1016/j.laa.2009.08.001 · Cited by 21

A Convex Optimization Approach for Computing Correlated Choice Probabilities With Many Alternatives

Ahipaşaoğlu, S. D., Li, X., & Natarajan, K. (2018) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2018.2875673 · Cited by 21

Splitting methods for time integration of trajectories in combined electric and magnetic fields

Knapp, C., Kendl, A., Koskela, A., & Ostermann, A. (2015) · Physical Review E · doi:10.1103/physreve.92.063310 · Cited by 21

A Padé family of iterations for the matrix sector function and the matrix p th root

Laszkiewicz, B., & Ziętak, K. (2009) · Numerical Linear Algebra with Applications · doi:10.1002/nla.656 · Cited by 21

Average energy dissipation rates of explicit exponential Runge-Kutta methods for gradient flow problems

Liao, H.-L., & Wang, X. (2024) · Mathematics of Computation · doi:10.1090/mcom/4015 · Cited by 20

1-D Filter for Ring Artifact Suppression

Titarenko, V. (2016) · IEEE Signal Processing Letters · doi:10.1109/lsp.2016.2554363 · Cited by 20

Increasing the Efficiency of Sparse Matrix-Matrix Multiplication with a 2.5D Algorithm and One-Sided MPI

Lazzaro, A., VandeVondele, J., Hutter, J., & Schütt, O. (2017) · Platform for Advanced Scientific Computing Conference (PASC) · doi:10.1145/3093172.3093228 · Cited by 20

Superiorization vs. accelerated convex optimization: The superiorized / regularized least-squares case

Censor, Y., Petra, S., & Schnörr, C. (2020) · Journal of Applied and Numerical Optimization · doi:10.23952/jano.2.2020.1.03 · Cited by 20

Effects of round-to-nearest and stochastic rounding in the numerical solution of the heat equation in low precision

Croci, M., & Giles, M. B. (2022) · IMA Journal of Numerical Analysis · doi:10.1093/imanum/drac012 · Cited by 20

Minimal Active Space: NOSCF and NOSI in Multistate Density Functional Theory

Lu, Y., Zhao, R., Zhang, J., Liu, M., & Gao, J. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c00908 · Cited by 20

Using the Restricted-denominator Rational Arnoldi Method for Exponential Integrators

Novati, P. (2011) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/100814202 · Cited by 20

Some Matrix Iterations for Computing Matrix Sign Function

Soleymani, F., Tohidi, E., Shateyi, S., & Haghani, F. K. (2014) · Journal of Applied Mathematics · doi:10.1155/2014/425654 · Cited by 20

The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential

Aprahamian, M., & Higham, N. J. (2014) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/130920137 · Cited by 20

A deflated conjugate gradient method for multiple right hand sides and multiple shifts

Birk, S., & Frommer, A. (2013) · Numerical Algorithms · doi:10.1007/s11075-013-9805-9 · Cited by 20

Matrix Probing and its Conditioning

Chiu, J., & Laurent Demanet, A. (2012) · SIAM Journal on Numerical Analysis · doi:10.1137/110825972 · Cited by 20

The simplified topological ε-algorithms: software and applications

Brezinski, C., & Redivo‐Zaglia, M. (2016) · Numerical Algorithms · doi:10.1007/s11075-016-0238-0 · Cited by 20

An output error bound for time-limited balanced truncation

Redmann, M., & Kürschner, P. (2018) · Systems & Control Letters · doi:10.1016/j.sysconle.2018.08.004 · Cited by 20

A graph theoretic approach for modelling tiger corridor network in Central India-Eastern Ghats landscape complex, India

Shanu, S., Idiculla, J., Qureshi, Q., Jhala, Y. V., Aggarwal, A., Dimri, P., & Bhattacharya, S. (2019) · Ecological Informatics · doi:10.1016/j.ecoinf.2019.01.002 · Cited by 20

The Generalized Ridge Estimator of the Inverse Covariance Matrix

van Wieringen, W. N. (2019) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.2019.1604374 · Cited by 20

Hermite Interpolation and Data Processing Errors on Riemannian Matrix Manifolds

Zimmermann, R. (2020) · SIAM Journal on Scientific Computing · doi:10.1137/19m1282878 · Cited by 20

Generalized Inverses Estimations by Means of Iterative Methods with Memory

Artidiello, S., Cordero, A., Torregrosa, J. R., & Vassileva, M. P. (2019) · Mathematics · doi:10.3390/math8010002 · Cited by 20

On The Stability of Polynomial Spectral Graph Filters

Kenlay, H., Thanou, D., & Dong, X. (2020) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp40776.2020.9054072 · Cited by 20

Some uses of the field of values in numerical analysis

Michele Benzi, A. (2020) · Bollettino Della Unione Matematica Italiana · doi:10.1007/s40574-020-00249-2 · Cited by 20

Certain Matrix Riemann–Liouville Fractional Integrals Associated with Functions Involving Generalized Bessel Matrix Polynomials

Abdalla, M., Akel, M. S., & Choi, J. (2021) · Symmetry · doi:10.3390/sym13040622 · Cited by 20

Mathematical modeling of multiple pathways in colorectal carcinogenesis using dynamical systems with Kronecker structure

Haupt, S., Zeilmann, A., Ahadova, A., Bläker, H., Doeberitz, M. V. K., Kloor, M., & Heuveline, V. (2021) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1008970 · Cited by 20

Computing Symplectic Eigenpairs of Symmetric Positive-Definite Matrices via Trace Minimization and Riemannian Optimization

Son, N. T., Absil, P.-A., Gao, B., & Stykel, T. (2021) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/21m1390621 · Cited by 20

Mapping directed networks

Crofts, J. J., Estrada, E., Higham, D. J., & Taylor, A. D. (2010) · Strathprints: The University of Strathclyde institutional repository (University of Strathclyde) · Cited by 20

Accurate Interactive Visualization of Large Deformations and Variability in Biomedical Image Ensembles

Hermann, M., Schunke, A. C., Schultz, T., & Klein, R. (2015) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2015.2467198 · Cited by 20

Symmetric spaces and Lie triple systems in numerical analysis of differential equations

Munthe–Kaas, H., Quispel, G. R. W., & Zanna, A. (2014) · BIT Numerical Mathematics · doi:10.1007/s10543-014-0473-5 · Cited by 20

Fast Structured Matrix Computations: Tensor Rank and Cohn–Umans Method

Ye, K., & Lim, L. (2016) · Foundations of Computational Mathematics · doi:10.1007/s10208-016-9332-x · Cited by 21

Computing Matrix Squareroot via Non Convex Local SearchPreprint

Jain, P., Jin, C., Kakade, S. M., & Netrapalli, P. (2015) · arXiv (Cornell University) · Cited by 20

GPU Accelerated Algorithms for Computing Matrix Function Vector Products with Applications to Exponential Integrators and Fractional Diffusion

Farquhar, M. E., Moroney, T. J., Yang, Q., & Turner, I. (2016) · SIAM Journal on Scientific Computing · doi:10.1137/15m1021672 · Cited by 19

Computing the Riemannian Logarithm on the Stiefel Manifold: Metrics, Methods, and Performance

Zimmermann, R., & Hüper, K. (2022) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/21m1425426 · Cited by 19

Usable and Precise Asymptotics for Generalized Linear Mixed Model Analysis and Design

Jiang, J., WAND, M. P., & Bhaskaran, A. (2021) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12473 · Cited by 19

An Exponential Time Differencing Runge–Kutta Method ETDRK32 for Phase Field Models

Cao, W., Yang, H., & Chen, W. (2024) · Journal of Scientific Computing · doi:10.1007/s10915-024-02474-9 · Cited by 19

Discretizing stochastic dynamical systems using Lyapunov equations

Wahlström, N., Axelsson, P., & Gustafsson, F. (2014) · IFAC Proceedings Volumes · doi:10.3182/20140824-6-za-1003.02157 · Cited by 19

Iterative methods for low rank approximation of graph similarity matrices

Cason, T., Absil, P.-A., & Dooren, P. M. V. (2012) · Linear Algebra and its Applications · doi:10.1016/j.laa.2011.12.004 · Cited by 19

On the Construction and Properties of $m$-step Methods for FDEs

Aceto, L., Magherini, C., & Novati, P. (2015) · SIAM Journal on Scientific Computing · doi:10.1137/140973505 · Cited by 19

Higher Order Fréchet Derivatives of Matrix Functions and the Level-2 Condition Number

Higham, N. J., & Relton, S. D. (2014) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/130945259 · Cited by 19

A matrix approach for partial differential equations with Riesz space fractional derivatives

Popolizio, M. (2013) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2013-01978-8 · Cited by 19

An Algorithm for the Matrix Lambert $W$ Function

Fasi, M., Higham, N. J., & Iannazzo, B. (2015) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/140997610 · Cited by 19

Parameterless Stopping Criteria for Recursive Density Matrix Expansions

Kruchinina, A., Rudberg, E., & Rubensson, E. H. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00626 · Cited by 19

On the exponential generating function for non-backtracking walks

Arrigo, F., Grindrod, P., Higham, D. J., & Noferini, V. (2018) · Linear Algebra and its Applications · doi:10.1016/j.laa.2018.07.010 · Cited by 19

A density matrix approach to the convergence of the self-consistent field iteration

Upadhyaya, P., Elias Jarlebring, A., & Rubensson, E. H. (2020) · Numerical Algebra Control and Optimization · doi:10.3934/naco.2020018 · Cited by 19

From microscopic price dynamics to multidimensional rough volatility models

Rosenbaum, M., & Tomas, M. (2021) · Advances in Applied Probability · doi:10.1017/apr.2020.60 · Cited by 19

Four-dimensional wind field generation for the aeroelastic simulation of wind turbines with lidars

Chen, Y., Guo, F., Schlipf, D., & Cheng, P. W. (2022) · Wind energy science · doi:10.5194/wes-7-539-2022 · Cited by 19

Exact solutions to a class of feedback systems on SO(n)

Markdahl, J., & Xiaoming Hu, A. (2015) · Automatica · doi:10.1016/j.automatica.2015.10.023 · Cited by 19

Analysis of Krylov subspace approximation to large-scale differential Riccati equations

Koskela, A., & Mena, H. (2020) · ETNA - Electronic Transactions on Numerical Analysis · doi:10.1553/etna_vol52s431 · Cited by 19

New block quadrature rules for the approximation of matrix functions

Lothar Reichel, B., Rodriguez, G., & Tang, T. (2015) · Linear Algebra and its Applications · doi:10.1016/j.laa.2015.07.007 · Cited by 19

Principal Component Projection Without Principal Component AnalysisPreprint

Frostig, R., Musco, C., Musco, C., & Sidford, A. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1602.06872 · Cited by 19

Doubling Algorithms with Permuted Lagrangian Graph Bases

Mehrmann, V., & Poloni, F. (2012) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/110850773 · Cited by 18

Estimation of the bilinear form y⁎f(A)x for Hermitian matrices

Fika, P., & Mitrouli, M. (2015) · Linear Algebra and its Applications · doi:10.1016/j.laa.2015.08.033 · Cited by 18

A geodesic feedback law to decouple the full and reduced attitude

Markdahl, J., Hoppe, J., Wang, L., & Xiaoming Hu, A. (2017) · Systems & Control Letters · doi:10.1016/j.sysconle.2017.01.005 · Cited by 18

Generalized linearization techniques in electrical impedance tomography

Hyvönen, N., & Mustonen, L. (2018) · Numerische Mathematik · doi:10.1007/s00211-018-0959-1 · Cited by 18

A multiquadric RBF–FD scheme for simulating the financial HHW equation utilizing exponential integrator

Soleymani, F., & Ullah, M. Z. (2018) · CALCOLO · doi:10.1007/s10092-018-0294-z · Cited by 18

Approximation of a fractional power of an elliptic operator

Vabishchevich, P. N. (2020) · Numerical Linear Algebra with Applications · doi:10.1002/nla.2287 · Cited by 18

The embedding problem for Markov matrices

Casanellas, M., Fernández-Sánchez, J., & Roca-Lacostena, J. (2022) · Publicacions Matemàtiques · doi:10.5565/publmat6712308 · Cited by 18

Stochastic time-dependent enzyme kinetics: Closed-form solution and transient bimodality

Holehouse, J., Sukys, A., & Grima, R. (2020) · The Journal of Chemical Physics · doi:10.1063/5.0017573 · Cited by 18

Preparation of Quantum Gates for Open Quantum Systems by Lyapunov Control Method

Wen, J., & Cong, S. (2016) · Open Systems & Information Dynamics · doi:10.1142/s1230161216500050 · Cited by 18

An efficient energy-preserving method for the two-dimensional fractional Schrödinger equation

Fu, Y., Xu, Z., Cai, W., & Wang, Y. (2021) · Applied Numerical Mathematics · doi:10.1016/j.apnum.2021.02.010 · Cited by 18

Why Approximate Matrix Square Root Outperforms Accurate SVD in Global Covariance Pooling?

Song, Y., Sebe, N., & Wang, W. (2021) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv48922.2021.00115 · Cited by 20

Inertial stochastic PALM and applications in machine learning

Hertrich, J., & Steidl, G. (2022) · Sampling Theory Signal Processing and Data Analysis · doi:10.1007/s43670-022-00021-x · Cited by 20

Taylor's theorem for matrix functions with applications to condition number estimation

Deadman, E., & Relton, S. D. (2016) · Linear Algebra and its Applications · doi:10.1016/j.laa.2016.04.010 · Cited by 18

An efficient and stable Newton-type iterative method for computing generalized inverse A T , S ( 2 ) $A_{T,S}^{(2)}$

Soleymani, F. (2014) · Numerical Algorithms · doi:10.1007/s11075-014-9913-1 · Cited by 18

Effectively unpaired electrons in bipartite lattices within the generalized tight-binding approximation: application to graphene nanoflakes

", S., & Luzanov, A. V. (2014) · Functional materials · doi:10.15407/fm21.04.437 · Cited by 18

Gradient Flows in Filtering and Fisher-Rao Geometry

Halder, A., & Georgiou, T. T. (2018) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc.2018.8431003 · Cited by 18

Randomized Linear Algebra Approaches to Estimate the Von Neumann Entropy of Density Matrices

Kontopoulou, E.-M., Dexter, G., Wojciech Szpankowski, A., Grama, A. Y., & Petros Drineas, B. (2018) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2018.8437723 · Cited by 18

A binary powering Schur algorithm for computing primary matrix roots

Greco, F., & Iannazzo, B. (2010) · Numerical Algorithms · doi:10.1007/s11075-009-9357-1 · Cited by 18

Logarithms and Square Roots of Real MatricesPreprint

Gallier, J. H. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0805.0245 · Cited by 18

MCMC for inference on phase-type and masked system lifetime models

Aslett, L. J. M. (2012) · Arrow@dit (Dublin Institute of Technology) · Cited by 18

On convergence of Krylov subspace approximations of time-invariant self-adjoint dynamical systems

Druskin, V. L., & Zaslavsky, M. (2011) · Linear Algebra and its Applications · doi:10.1016/j.laa.2011.02.039 · Cited by 17

An autocorrelation method for three-dimensional strain analysis

Thissen, C., & Brandon, M. T. (2015) · Journal of Structural Geology · doi:10.1016/j.jsg.2015.09.001 · Cited by 17

Automatic method for synchronizing workpiece frames in twin-robot nondestructive testing system

Lu, Z., Xu, C., Pan, Q., Meng, F., & Li, X. (2015) · Chinese Journal of Mechanical Engineering · doi:10.3901/cjme.2015.0424.064 · Cited by 17

An algorithm to compute the polar decomposition of a 3 × 3 matrix

Higham, N. J., & Noferini, V. (2016) · Numerical Algorithms · doi:10.1007/s11075-016-0098-7 · Cited by 17

A calibration method for non-positive definite covariance matrix in multivariate data analysis

Huang, C., Farewell, D. M., & Pan, J. (2017) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2017.03.001 · Cited by 17

Covariances in Computer Vision and Machine Learning

Minh, H. Q., & Murino, V. (2017) · Synthesis lectures on computer vision · doi:10.2200/s00801ed1v01y201709cov011 · Cited by 17

Sparsity preserving optimal control of discretized PDE systems

Haber, A., & Verhaegen, M. (2018) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2018.01.034 · Cited by 17

Optimality of the Paterson–Stockmeyer method for evaluating matrix polynomials and rational matrix functions

Fasi, M. (2019) · Linear Algebra and its Applications · doi:10.1016/j.laa.2019.04.001 · Cited by 17

Wilkinson’s Bus: Weak Condition Numbers, with an Application to Singular Polynomial Eigenproblems

Lotz, M., & Noferini, V. (2020) · Foundations of Computational Mathematics · doi:10.1007/s10208-020-09455-y · Cited by 17

Gaussian process assisted stochastic dynamic analysis with applications to near-periodic structures

Chatterjee, T., Karličić, D., Adhikari, S., & Friswell, M. I. (2020) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2020.107218 · Cited by 17

Toward Faster and Simpler Matrix Normalization via Rank-1 Update

Yu, T., Cai, Y., & Li, P. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-58529-7_13 · Cited by 18

High-order numerical solutions to the shallow-water equations on the rotated cubed-sphere grid

Gaudreault, S., Charron, M., Dallerit, V., & Tokman, M. (2021) · Journal of Computational Physics · doi:10.1016/j.jcp.2021.110792 · Cited by 17

Communication in complex networks

Cabrera, O. D. L. C., Jin, J., Noschese, S., & Lothar Reichel, B. (2021) · Applied Numerical Mathematics · doi:10.1016/j.apnum.2021.10.005 · Cited by 17

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