## Higham, Desmond J.

Compute Distance To:
 Author ID: higham.desmond-j Published as: Higham, Desmond J.; Higham, D. J.; Higham, Desmond J more...less Homepage: https://www.maths.ed.ac.uk/~dhigham/ External Links: MGP · ORCID · Wikidata · Google Scholar · dblp · IdRef
 Documents Indexed: 127 Publications since 1988, including 10 Books 1 Contribution as Editor · 2 Further Contributions Co-Authors: 62 Co-Authors with 95 Joint Publications 1,560 Co-Co-Authors
all top 5

### Co-Authors

 32 single-authored 11 Mao, Xuerong 10 Grindrod, Peter 10 Higham, Nicholas J. 7 Arrigo, Francesca 7 Griffiths, David F. 7 Noferini, Vanni 6 Kalna, Gabriela 6 Stuart, Andrew M. 5 Anderson, David Frederick 5 Kloeden, Peter Eris 4 Szpruch, Lukasz 4 Vass, J. Keith 3 Aves, Mark A. 3 Chalmers, Graeme D. 3 Estrada, Ernesto 3 Intep, Somkid 3 Sun, Yu 2 Calvo, Manuel 2 Crofts, Jonathan J. 2 Khanin, Raya 2 Mantzaris, Alexander V. 2 Montijano, Juan Ignacio 2 Rández, Luis 2 Sardar, Tasneem K. 2 Taylor, Alan M. 2 Tudisco, Francesco 2 Yuan, Chenggui 1 Adams, Ryan Prescott 1 Akartunalı, Kerem 1 Alsayed, Ahmad 1 Anaya-Izquierdo, Karim Alejandro 1 Archambeau, Cédric 1 Barclay, Graeme J. 1 Bartels, Sven G. 1 Barthelmé, Simon 1 Beffy, Magali 1 Beskos, Alexandros 1 Bhadra, Anindya 1 Blanchard, Pierre 1 Bornn, Luke 1 Bouchard, Guillaume 1 Boys, Richard J. 1 Bryden, Alan 1 Calderhead, Ben 1 Campbell, David A. 1 Cao, Jiguo 1 Chen, Yanjiun 1 Chin, Siu A. 1 Chopin, Nicolas 1 Christie, Mike 1 Coolen, Anthony C. C. 1 Cornebise, Julien 1 Cox, David Roxbee 1 Critchley, Frank 1 Davies, Penny J. 1 Doucet, Arnaud 1 Draper, David 1 Dryden, Ian L. 1 Eguchi, Shinto 1 Enright, Wayne H. 1 Famelis, Ioannis Th. 1 Fearnhead, Paul 1 Fenu, Caterina 1 Filippone, Maurizio 1 Fox, Maria 1 Friel, Nial 1 Gelman, Andrew 1 Giles, Michael B. 1 Girolami, Mark A. 1 Golightly, Andrew 1 Griffin, Jim E. 1 Gripton, Adam 1 Guerrera, Thiago 1 Guillas, Serge 1 Gutenkunst, Ryan 1 Haario, Heikki 1 Higham, Catherine F. 1 Holmes, Christopher C. 1 Honkela, Antti 1 Humphries, Antony R. 1 Husmeier, Dirk 1 Ikeda, Shiro 1 Jacob, Pierre E. 1 Jasra, Ajay 1 Johansen, Adam M. 1 Jupp, Peter E. 1 Kibble, Milla 1 Kypraios, Theodore 1 Laflin, Peter 1 Latuszynski, Krzysztof 1 Leite, Saul C. 1 Machta, Benjamin B. 1 Mansinghka, Vikash K. 1 Marin, Jean-Michel 1 Marriott, Paul 1 Mattingly, Jonathan Christopher 1 McDonald, Edward J. 1 Meng, Xiaoli 1 Mira, Antonietta 1 Murray, Iain ...and 49 more Co-Authors
all top 5

### Serials

 10 BIT 9 SIAM Journal on Matrix Analysis and Applications 8 IMA Journal of Numerical Analysis 8 SIAM Journal on Numerical Analysis 7 Journal of Computational and Applied Mathematics 7 Applied Numerical Mathematics 7 SIAM Review 5 Multiscale Modeling & Simulation 4 Linear Algebra and its Applications 3 Numerische Mathematik 3 SIAM Journal on Scientific Computing 3 LMS Journal of Computation and Mathematics 3 Discrete and Continuous Dynamical Systems. Series B 2 ACM Transactions on Mathematical Software 2 SIAM Journal on Scientific and Statistical Computing 2 European Journal of Applied Mathematics 2 International Journal of Computer Mathematics 2 ETNA. Electronic Transactions on Numerical Analysis 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Internet Mathematics 2 Journal of Complex Networks 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Other Titles in Applied Mathematics 1 IMA Journal of Applied Mathematics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Computational Physics 1 Chaos, Solitons and Fractals 1 Theoretical Computer Science 1 Applied Mathematics Letters 1 Journal of Scientific Computing 1 AI Communications 1 SIAM Journal on Applied Mathematics 1 Stochastic Processes and their Applications 1 Advances in Computational Mathematics 1 Journal of Difference Equations and Applications 1 Finance and Stochastics 1 Chaos 1 Journal of the Royal Statistical Society. Series B. Statistical Methodology 1 IMA Journal of Management Mathematics 1 Mathematical Medicine and Biology 1 International Journal of Numerical Analysis and Modeling 1 The Open Applied Mathematics Journal 1 SIAM/ASA Journal on Uncertainty Quantification 1 Springer Undergraduate Mathematics Series 1 SIAM Journal on Mathematics of Data Science
all top 5

### Fields

 94 Numerical analysis (65-XX) 42 Ordinary differential equations (34-XX) 38 Probability theory and stochastic processes (60-XX) 25 Combinatorics (05-XX) 20 Computer science (68-XX) 19 Biology and other natural sciences (92-XX) 18 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 8 Operations research, mathematical programming (90-XX) 7 Dynamical systems and ergodic theory (37-XX) 6 Statistics (62-XX) 4 Partial differential equations (35-XX) 3 General and overarching topics; collections (00-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX) 1 Classical thermodynamics, heat transfer (80-XX)

### Citations contained in zbMATH Open

119 Publications have been cited 3,158 times in 2,209 Documents Cited by Year
An algorithmic introduction to numerical simulation of stochastic differential equations. Zbl 0979.65007
Higham, Desmond J.
2001
Strong convergence of Euler-type methods for nonlinear stochastic differential equations. Zbl 1026.65003
Higham, Desmond J.; Mao, Xuerong; Stuart, Andrew M.
2002
Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise. Zbl 1075.60072
Mattingly, J. C.; Stuart, A. M.; Higham, D. J.
2002
Mean-square and asymptotic stability of the stochastic theta method. Zbl 0982.60051
Higham, Desmond J.
2000
Riemann manifold Langevin and Hamiltonian Monte Carlo methods. With discussion and authors’ reply. Zbl 1411.62071
2011
Numerical methods for nonlinear stochastic differential equations with jumps. Zbl 1186.65010
Higham, Desmond J.; Kloeden, Peter. E.
2005
Network properties revealed through matrix functions. Zbl 1214.05077
2010
Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations. Zbl 1144.65005
Higham, Desmond J.; Mao, Xuerong; Yuan, Chenggui
2007
Exponential mean-square stability of numerical solutions to stochastic differential equations. Zbl 1055.65009
Higham, Desmond J.; Mao, Xuerong; Stuart, Andrew M.
2003
Convergence and stability of implicit methods for jump-diffusion systems. Zbl 1109.65007
Higham, Desmond J.; Kloeden, Peter E.
2006
$$A$$-stability and stochastic mean-square stability. Zbl 0961.65003
Higham, Desmond J.
2000
Structured backward error and condition of generalized eigenvalue problems. Zbl 0935.65032
Higham, Desmond J.; Higham, Nicholas J.
1998
Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems. Zbl 1128.65007
Higham, Desmond J.; Kloeden, Peter E.
2007
Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model. Zbl 1230.65011
Szpruch, Lukasz; Mao, Xuerong; Higham, Desmond J.; Pan, Jiazhu
2011
Numerical methods for ordinary differential equations. Initial value problems. Zbl 1209.65070
Griffiths, David F.; Higham, Desmond J.
2010
Backward error and condition of structured linear systems. Zbl 0747.65028
Higham, Desmond J.; Higham, Nicholas J.
1992
Multilevel Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics. Zbl 1262.60072
Anderson, David F.; Higham, Desmond J.
2012
Modeling and simulating chemical reactions. Zbl 1144.80011
Higham, Desmond J.
2008
Condition numbers and their condition numbers. Zbl 0816.15004
Higham, Desmond J.
1995
Convergence, nonnegativity and stability of a new Milstein scheme with applications to finance. Zbl 1279.60068
Higham, Desmond J.; Mao, Xuerong; Szpruch, Lukasz
2013
Numerical simulation of a linear stochastic oscillator with additive noise. Zbl 1060.65007
Strømmen Melbø, Aslaug H.; Higham, Desmond J.
2004
An introduction to financial option valuation. Mathematics, stochastics and computation. Zbl 1122.91001
Higham, Desmond J.
2004
Trust region algorithms and timestep selection. Zbl 0945.65068
Higham, Desmond J.
1999
Stiffness of ODEs. Zbl 0782.65091
Higham, Desmond J.; Trefethen, Lloyd N.
1993
Analyzing multi-level Monte Carlo for options with non-globally Lipschitz payoff. Zbl 1199.65008
Giles, Michael B.; Higham, Desmond J.; Mao, Xuerong
2009
Existence and stability of fixed points for a discretised nonlinear reaction-diffusion equation with delay. Zbl 0834.65079
Higham, Desmond J.; Sardar, Tasneem
1995
Global error versus tolerance for explicit Runge-Kutta methods. Zbl 0738.65073
Higham, Desmond J.
1991
Stochastic ordinary differential equations in applied and computational mathematics. Zbl 1221.60099
Higham, Desmond J.
2011
On the boundedness of asymptotic stability regions for the stochastic theta method. Zbl 1026.65004
Bryden, Alan; Higham, Desmond J.
2003
Preserving exponential mean-square stability in the simulation of hybrid stochastic differential equations. Zbl 1137.65007
Higham, Desmond J.; Mao, Xuerong; Yuan, Chenggui
2007
Large growth factors in Gaussian elimination with pivoting. Zbl 0681.65012
Higham, Nicholas J.; Higham, Desmond J.
1989
Complexity of multilevel Monte Carlo tau-leaping. Zbl 1327.60136
Anderson, David F.; Higham, Desmond J.; Sun, Yu
2014
Componentwise perturbation theory for linear systems with multiple right- hand sides. Zbl 0801.65043
Higham, Desmond J.; Higham, Nicholas J.
1992
Asymptotic stability of a jump-diffusion equation and its numerical approximation. Zbl 1190.65010
Chalmers, Graeme D.; Higham, Desmond J.
2008
Stepsize selection for tolerance proportionality in explicit Runge-Kutta codes. Zbl 0891.65097
Calvo, M.; Higham, D. J.; Montijano, J. I.; Rández, L.
1997
Matlab guide. 2nd ed. Zbl 1067.68180
Higham, Desmond J; Higham, Nicholas J.
2005
Deep learning: an introduction for applied mathematicians. Zbl 1440.68214
Higham, Catherine F.; Higham, Desmond J.
2019
Convergence and stability analysis for implicit simulations of stochastic differential equations with random jump magnitudes. Zbl 1148.65005
Chalmers, Graeme D.; Higham, Desmond J.
2008
Analysis of stepsize selection schemes for Runge-Kutta codes. Zbl 0661.65077
Hall, G.; Higham, D. J.
1988
Robust defect control with Runge-Kutta schemes. Zbl 0682.65033
Higham, Desmond J.
1989
Parallel defect control. Zbl 0743.65069
Enright, W. H.; Higham, D. J.
1991
Mean exit times and the multilevel Monte Carlo method. Zbl 1282.65020
Higham, Desmond J.; Mao, Xuerong; Roj, Mikolaj; Song, Qingshuo; Yin, George
2013
The tolerance proportionality of adaptive ODE solvers. Zbl 0780.65050
Higham, Desmond J.
1993
A matrix iteration for dynamic network summaries. Zbl 1262.91121
Grindrod, Peter; Higham, Desmond J.
2013
Runge-Kutta defect control using Hermite-Birkhoff interpolation. Zbl 0745.65051
Higham, Desmond J.
1991
A dynamical systems view of network centrality. Zbl 1371.90039
Grindrod, Peter; Higham, Desmond J.
2014
Matlab guide. Zbl 0953.68642
Higham, Desmond J.; Higham, Nicholas J.
2000
Spectral clustering and its use in bioinformatics. Zbl 1123.65024
Higham, Desmond J.; Kalna, Gabriela; Kibble, Milla
2007
Runge-Kutta type methods for orthogonal integration. Zbl 0866.65047
Higham, Desmond J.
1996
Time-stepping and preserving orthonormality. Zbl 0891.65082
Higham, Desmond J.
1997
Nonnormality and stochastic differential equations. Zbl 1105.65007
Higham, D. J.; Mao, X.
2006
Betweenness in time dependent networks. Zbl 1352.90020
2015
Comparing hitting time behavior of Markov jump processes and their diffusion approximations. Zbl 1202.60138
Szpruch, Lukasz; Higham, Desmond J.
2010
Network science. Complexity in nature and technology. Zbl 1202.68024
2010
Mapping directed networks. Zbl 1205.65166
Crofts, Jonathan J.; Estrada, Ernesto; Higham, Desmond J.; Taylor, Alan
2010
Analysis of the Enright-Kamel partitioning method for stiff ordinary differential equations. Zbl 0659.65069
Higham, Desmond J.
1989
The deformed graph Laplacian and its applications to network centrality analysis. Zbl 1381.05043
Grindrod, Peter; Higham, Desmond J.; Noferini, Vanni
2018
Evolving graphs: dynamical models, inverse problems and propagation. Zbl 1195.05075
Grindrod, Peter; Higham, Desmond J.
2010
On the exponential generating function for non-backtracking walks. Zbl 1394.05119
Arrigo, Francesca; Grindrod, Peter; Higham, Desmond J.; Noferini, Vanni
2018
Multilevel Monte Carlo for stochastic differential equations with small noise. Zbl 1334.60128
Anderson, David F.; Higham, Desmond J.; Sun, Yu
2016
Does error control suppress spuriosity? Zbl 0873.65083
Aves, Mark A.; Griffiths, David F.; Higham, Desmond J.
1997
Dynamics of constant and variable stepsize methods for a nonlinear population model with delay. Zbl 0899.92027
Sardar, Tasneem K.; Higham, Desmond J.
1997
Global error estimation with adaptive explicit Runge-Kutta methods. Zbl 0840.65087
Calvo, M.; Higham, D. J.; Montijano, J. I.; Rández, L.
1996
Matlab guide. 3rd revised and updated edition. Zbl 1357.68001
Higham, Desmond J; Higham, Nicholas J.
2017
Nine ways to implement the binomial method for option valuation in MATLAB. Zbl 1029.91030
Higham, Desmond J.
2002
Highly continuous Runge-Kutta interpolants. Zbl 0900.65235
Higham, D. J.
1991
First and second moment reversion for a discretized square root process with jumps. Zbl 1188.91241
Chalmers, Graeme D.; Higham, Desmond J.
2010
Monotonic piecewise cubic interpolation, with applications to ODE plotting. Zbl 0768.65002
Higham, D. J.
1992
Discovering bipartite substructure in directed networks. Zbl 1223.68087
Taylor, Alan; Vass, J. Keith; Higham, Desmond J.
2011
A matrix perturbation view of the small world phenomenon. Zbl 1050.65004
Higham, Desmond J.
2003
The structured sensitivity of Vandermonde-like systems. Zbl 0766.65042
Bartels, Sven G.; Higham, Desmond J.
1992
Analysis of the dynamics of local error control via a piecewise continuous residual. Zbl 0907.65077
Higham, D. J.; Stuart, A. M.
1998
A matrix perturbation view of the small world phenomenon. Zbl 1119.65008
Higham, Desmond J.
2007
Block matrix formulations for evolving networks. Zbl 1362.05120
Fenu, Caterina; Higham, Desmond J.
2017
Unravelling small world networks. Zbl 1028.65034
Higham, Desmond J.
2003
A clustering coefficient for weighted networks, with application to gene expression data. Zbl 1189.68084
Kalna, Gabriela; Higham, Desmond J.
2007
Embedded Runge-Kutta formulae with stable equilibrium states. Zbl 0704.65054
Higham, D. J.; Hall, G.
1990
Googling the brain: discovering hierarchical and asymmetric network structures, with applications in neuroscience. Zbl 1245.05118
Crofts, Jonathan J.; Higham, Desmond J.
2011
Non-backtracking walk centrality for directed networks. Zbl 1460.90040
Arrigo, Francesca; Grindrod, Peter; Higham, Desmond J.; Noferini, Vanni
2018
Regular Runge-Kutta pairs. Zbl 0890.65076
Higham, Desmond J.
1997
Equilibrium states of adaptive algorithms for delay differential equations. Zbl 0833.65070
Higham, Desmond J.; Famelis, Ioannis Th.
1995
Error analysis of QR algorithms for computing Lyapunov exponents. Zbl 1022.65079
McDonald, Edward J.; Higham, Desmond J.
2001
Chemical master equation and Langevin regimes for a gene transcription model. Zbl 1151.92012
Khanin, Raya; Higham, Desmond J.
2008
Analysis of the singular value decomposition as a tool for processing microarray expression data. Zbl 1183.68533
Higham, Desmond J.; Kalna, Gabriela; Vass, J. Keith
2005
Switching and diffusion models for gene regulation networks. Zbl 1184.92016
Intep, Somkid; Higham, Desmond J.; Mao, Xuerong
2009
Greedy pathlengths and small world graphs. Zbl 1095.68083
Higham, Desmond J.
2006
Centrality analysis for modified lattices. Zbl 1373.05186
Paton, Martin; Akartunali, Kerem; Higham, Desmond J.
2017
Non-backtracking alternating walks. Zbl 1422.05061
Arrigo, Francesca; Higham, Desmond J.; Noferini, Vanni
2019
Defect estimation in Adams PECE codes. Zbl 0676.65082
Higham, Desmond J.
1989
Non-backtracking PageRank. Zbl 1425.65046
Arrigo, Francesca; Higham, Desmond J.; Noferini, Vanni
2019
A nonlinear spectral method for core-periphery detection in networks. Zbl 07468807
Tudisco, Francesco; Higham, Desmond J.
2019
Nonnormality effects in a discretised nonlinear reaction-convection-diffusion equation. Zbl 0853.65088
Higham, Desmond J.; Owren, Brynjulf
1996
Spectral analysis of two-signed microarray expression data. Zbl 1148.92016
Higham, Desmond J.; Kalna, Gabriela; Vass, J. Keith
2007
An introduction to multilevel Monte Carlo for option valuation. Zbl 1335.91102
Higham, Desmond J.
2015
The effect of quadrature on the dynamics of a discretized nonlinear integro-differential equation. Zbl 0946.65136
Aves, Mark A.; Davies, Penny J.; Higham, Desmond J.
2000
Phase space error control for dynamical systems. Zbl 0963.65140
Higham, D. J.; Humphries, A. R.; Wain, R. J.
2000
Runge-Kutta solutions of a hyperbolic conservation law with source term. Zbl 0966.65063
Aves, Mark A.; Griffiths, David F.; Higham, Desmond J.
2000
Qualitative properties of modified equations. Zbl 0935.34003
Gonzalez, O.; Higham, D. J.; Stuart, A. M.
1999
Error control for initial value problems with discontinuities and delays. Zbl 0781.65061
Higham, Desmond J.
1993
The dynamics of a discretised nonlinear delay differential equation. Zbl 0797.65053
Higham, D. J.
1994
Accurately computing the log-sum-exp and softmax functions. Zbl 07528305
Blanchard, Pierre; Higham, Desmond J.; Higham, Nicholas J.
2021
An introduction to the numerical simulation of stochastic differential equations. Zbl 07335009
Higham, Desmond J.; Kloeden, Peter E.
2021
Random matrices generating large growth in LU factorization with pivoting. Zbl 1459.65036
Higham, Desmond J.; Higham, Nicholas J.; Pranesh, Srikara
2021
Beyond non-backtracking: non-cycling network centrality measures. Zbl 1472.05081
Arrigo, Francesca; Higham, Desmond J.; Noferini, Vanni
2020
A framework for second-order eigenvector centralities and clustering coefficients. Zbl 1472.65043
Arrigo, Francesca; Higham, Desmond J.; Tudisco, Francesco
2020
Deep learning: an introduction for applied mathematicians. Zbl 1440.68214
Higham, Catherine F.; Higham, Desmond J.
2019
Non-backtracking alternating walks. Zbl 1422.05061
Arrigo, Francesca; Higham, Desmond J.; Noferini, Vanni
2019
Non-backtracking PageRank. Zbl 1425.65046
Arrigo, Francesca; Higham, Desmond J.; Noferini, Vanni
2019
A nonlinear spectral method for core-periphery detection in networks. Zbl 07468807
Tudisco, Francesco; Higham, Desmond J.
2019
On constrained Langevin equations and (bio)chemical reaction networks. Zbl 1481.60146
Anderson, David F.; Higham, Desmond J.; Leite, Saul C.; Williams, Ruth J.
2019
The deformed graph Laplacian and its applications to network centrality analysis. Zbl 1381.05043
Grindrod, Peter; Higham, Desmond J.; Noferini, Vanni
2018
On the exponential generating function for non-backtracking walks. Zbl 1394.05119
Arrigo, Francesca; Grindrod, Peter; Higham, Desmond J.; Noferini, Vanni
2018
Non-backtracking walk centrality for directed networks. Zbl 1460.90040
Arrigo, Francesca; Grindrod, Peter; Higham, Desmond J.; Noferini, Vanni
2018
Computational complexity analysis for Monte Carlo approximations of classically scaled population processes. Zbl 1401.60130
Anderson, David F.; Higham, Desmond J.; Sun, Yu
2018
Matlab guide. 3rd revised and updated edition. Zbl 1357.68001
Higham, Desmond J; Higham, Nicholas J.
2017
Block matrix formulations for evolving networks. Zbl 1362.05120
Fenu, Caterina; Higham, Desmond J.
2017
Centrality analysis for modified lattices. Zbl 1373.05186
Paton, Martin; Akartunali, Kerem; Higham, Desmond J.
2017
Multilevel Monte Carlo for stochastic differential equations with small noise. Zbl 1334.60128
Anderson, David F.; Higham, Desmond J.; Sun, Yu
2016
Inverse network sampling to explore online brand allegiance. Zbl 1408.91177
Grindrod, Peter; Higham, Desmond J.; Laflin, Peter; Otley, Amanda; Ward, Jonathan A.
2016
Betweenness in time dependent networks. Zbl 1352.90020
2015
An introduction to multilevel Monte Carlo for option valuation. Zbl 1335.91102
Higham, Desmond J.
2015
Complexity of multilevel Monte Carlo tau-leaping. Zbl 1327.60136
Anderson, David F.; Higham, Desmond J.; Sun, Yu
2014
A dynamical systems view of network centrality. Zbl 1371.90039
Grindrod, Peter; Higham, Desmond J.
2014
Convergence, nonnegativity and stability of a new Milstein scheme with applications to finance. Zbl 1279.60068
Higham, Desmond J.; Mao, Xuerong; Szpruch, Lukasz
2013
Mean exit times and the multilevel Monte Carlo method. Zbl 1282.65020
Higham, Desmond J.; Mao, Xuerong; Roj, Mikolaj; Song, Qingshuo; Yin, George
2013
A matrix iteration for dynamic network summaries. Zbl 1262.91121
Grindrod, Peter; Higham, Desmond J.
2013
Multilevel Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics. Zbl 1262.60072
Anderson, David F.; Higham, Desmond J.
2012
Bistability through triadic closure. Zbl 1258.05115
Grindrod, Peter; Higham, Desmond J.; Parsons, Mark C.
2012
Models for evolving networks: with applications in telecommunication and online activities. Zbl 1248.90032
Grindrod, Peter; Higham, Desmond J.
2012
Riemann manifold Langevin and Hamiltonian Monte Carlo methods. With discussion and authors’ reply. Zbl 1411.62071
2011
Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model. Zbl 1230.65011
Szpruch, Lukasz; Mao, Xuerong; Higham, Desmond J.; Pan, Jiazhu
2011
Stochastic ordinary differential equations in applied and computational mathematics. Zbl 1221.60099
Higham, Desmond J.
2011
Discovering bipartite substructure in directed networks. Zbl 1223.68087
Taylor, Alan; Vass, J. Keith; Higham, Desmond J.
2011
Googling the brain: discovering hierarchical and asymmetric network structures, with applications in neuroscience. Zbl 1245.05118
Crofts, Jonathan J.; Higham, Desmond J.
2011
Hybrid simulation of autoregulation within transcription and translation. Zbl 1211.92020
Higham, Desmond J.; Intep, Somkid; Mao, Xuerong; Szpruch, Lukasz
2011
Network properties revealed through matrix functions. Zbl 1214.05077
2010
Numerical methods for ordinary differential equations. Initial value problems. Zbl 1209.65070
Griffiths, David F.; Higham, Desmond J.
2010
Comparing hitting time behavior of Markov jump processes and their diffusion approximations. Zbl 1202.60138
Szpruch, Lukasz; Higham, Desmond J.
2010
Network science. Complexity in nature and technology. Zbl 1202.68024
2010
Mapping directed networks. Zbl 1205.65166
Crofts, Jonathan J.; Estrada, Ernesto; Higham, Desmond J.; Taylor, Alan
2010
Evolving graphs: dynamical models, inverse problems and propagation. Zbl 1195.05075
Grindrod, Peter; Higham, Desmond J.
2010
First and second moment reversion for a discretized square root process with jumps. Zbl 1188.91241
Chalmers, Graeme D.; Higham, Desmond J.
2010
Zero, one and two-switch models of gene regulation. Zbl 1201.37114
Intep, Somkid; Higham, Desmond J.
2010
Analyzing multi-level Monte Carlo for options with non-globally Lipschitz payoff. Zbl 1199.65008
Giles, Michael B.; Higham, Desmond J.; Mao, Xuerong
2009
Switching and diffusion models for gene regulation networks. Zbl 1184.92016
Intep, Somkid; Higham, Desmond J.; Mao, Xuerong
2009
Modeling and simulating chemical reactions. Zbl 1144.80011
Higham, Desmond J.
2008
Asymptotic stability of a jump-diffusion equation and its numerical approximation. Zbl 1190.65010
Chalmers, Graeme D.; Higham, Desmond J.
2008
Convergence and stability analysis for implicit simulations of stochastic differential equations with random jump magnitudes. Zbl 1148.65005
Chalmers, Graeme D.; Higham, Desmond J.
2008
Chemical master equation and Langevin regimes for a gene transcription model. Zbl 1151.92012
Khanin, Raya; Higham, Desmond J.
2008
Multidimensional partitioning and bi-partitioning: Analysis and application to gene expression data sets. Zbl 1138.65029
Kalna, Gabriela; Vass, J. Keith; Higham, Desmond J.
2008
Chemical master versus chemical Langevin for first-order reaction networks. Zbl 1322.92089
Higham, Desmond J.; Khanin, Raya
2008
Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations. Zbl 1144.65005
Higham, Desmond J.; Mao, Xuerong; Yuan, Chenggui
2007
Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems. Zbl 1128.65007
Higham, Desmond J.; Kloeden, Peter E.
2007
Preserving exponential mean-square stability in the simulation of hybrid stochastic differential equations. Zbl 1137.65007
Higham, Desmond J.; Mao, Xuerong; Yuan, Chenggui
2007
Spectral clustering and its use in bioinformatics. Zbl 1123.65024
Higham, Desmond J.; Kalna, Gabriela; Kibble, Milla
2007
A matrix perturbation view of the small world phenomenon. Zbl 1119.65008
Higham, Desmond J.
2007
A clustering coefficient for weighted networks, with application to gene expression data. Zbl 1189.68084
Kalna, Gabriela; Higham, Desmond J.
2007
Spectral analysis of two-signed microarray expression data. Zbl 1148.92016
Higham, Desmond J.; Kalna, Gabriela; Vass, J. Keith
2007
Convergence and stability of implicit methods for jump-diffusion systems. Zbl 1109.65007
Higham, Desmond J.; Kloeden, Peter E.
2006
Nonnormality and stochastic differential equations. Zbl 1105.65007
Higham, D. J.; Mao, X.
2006
Greedy pathlengths and small world graphs. Zbl 1095.68083
Higham, Desmond J.
2006
Numerical methods for nonlinear stochastic differential equations with jumps. Zbl 1186.65010
Higham, Desmond J.; Kloeden, Peter. E.
2005
Matlab guide. 2nd ed. Zbl 1067.68180
Higham, Desmond J; Higham, Nicholas J.
2005
Analysis of the singular value decomposition as a tool for processing microarray expression data. Zbl 1183.68533
Higham, Desmond J.; Kalna, Gabriela; Vass, J. Keith
2005
Google PageRank as mean playing time for pinball on the reverse web. Zbl 1083.68509
Higham, Desmond J.
2005
Spectral reordering of a range-dependent weighted random graph. Zbl 1077.92001
Higham, Desmond J.
2005
Numerical simulation of a linear stochastic oscillator with additive noise. Zbl 1060.65007
Strømmen Melbø, Aslaug H.; Higham, Desmond J.
2004
An introduction to financial option valuation. Mathematics, stochastics and computation. Zbl 1122.91001
Higham, Desmond J.
2004
Exponential mean-square stability of numerical solutions to stochastic differential equations. Zbl 1055.65009
Higham, Desmond J.; Mao, Xuerong; Stuart, Andrew M.
2003
On the boundedness of asymptotic stability regions for the stochastic theta method. Zbl 1026.65004
Bryden, Alan; Higham, Desmond J.
2003
A matrix perturbation view of the small world phenomenon. Zbl 1050.65004
Higham, Desmond J.
2003
Unravelling small world networks. Zbl 1028.65034
Higham, Desmond J.
2003
Strong convergence of Euler-type methods for nonlinear stochastic differential equations. Zbl 1026.65003
Higham, Desmond J.; Mao, Xuerong; Stuart, Andrew M.
2002
Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise. Zbl 1075.60072
Mattingly, J. C.; Stuart, A. M.; Higham, D. J.
2002
Nine ways to implement the binomial method for option valuation in MATLAB. Zbl 1029.91030
Higham, Desmond J.
2002
An algorithmic introduction to numerical simulation of stochastic differential equations. Zbl 0979.65007
Higham, Desmond J.
2001
Error analysis of QR algorithms for computing Lyapunov exponents. Zbl 1022.65079
McDonald, Edward J.; Higham, Desmond J.
2001
Mean-square and asymptotic stability of the stochastic theta method. Zbl 0982.60051
Higham, Desmond J.
2000
$$A$$-stability and stochastic mean-square stability. Zbl 0961.65003
Higham, Desmond J.
2000
Matlab guide. Zbl 0953.68642
Higham, Desmond J.; Higham, Nicholas J.
2000
The effect of quadrature on the dynamics of a discretized nonlinear integro-differential equation. Zbl 0946.65136
Aves, Mark A.; Davies, Penny J.; Higham, Desmond J.
2000
Phase space error control for dynamical systems. Zbl 0963.65140
Higham, D. J.; Humphries, A. R.; Wain, R. J.
2000
Runge-Kutta solutions of a hyperbolic conservation law with source term. Zbl 0966.65063
Aves, Mark A.; Griffiths, David F.; Higham, Desmond J.
2000
Theta method dynamics. Zbl 0953.65054
Barclay, Graeme J.; Griffiths, David F.; Higham, Desmond J.
2000
Trust region algorithms and timestep selection. Zbl 0945.65068
Higham, Desmond J.
1999
Qualitative properties of modified equations. Zbl 0935.34003
Gonzalez, O.; Higham, D. J.; Stuart, A. M.
1999
Structured backward error and condition of generalized eigenvalue problems. Zbl 0935.65032
Higham, Desmond J.; Higham, Nicholas J.
1998
Analysis of the dynamics of local error control via a piecewise continuous residual. Zbl 0907.65077
Higham, D. J.; Stuart, A. M.
1998
Stepsize selection for tolerance proportionality in explicit Runge-Kutta codes. Zbl 0891.65097
Calvo, M.; Higham, D. J.; Montijano, J. I.; Rández, L.
1997
Time-stepping and preserving orthonormality. Zbl 0891.65082
Higham, Desmond J.
1997
Does error control suppress spuriosity? Zbl 0873.65083
Aves, Mark A.; Griffiths, David F.; Higham, Desmond J.
1997
Dynamics of constant and variable stepsize methods for a nonlinear population model with delay. Zbl 0899.92027
Sardar, Tasneem K.; Higham, Desmond J.
1997
Regular Runge-Kutta pairs. Zbl 0890.65076
Higham, Desmond J.
1997
Runge-Kutta type methods for orthogonal integration. Zbl 0866.65047
Higham, Desmond J.
1996
Global error estimation with adaptive explicit Runge-Kutta methods. Zbl 0840.65087
Calvo, M.; Higham, D. J.; Montijano, J. I.; Rández, L.
1996
Nonnormality effects in a discretised nonlinear reaction-convection-diffusion equation. Zbl 0853.65088
Higham, Desmond J.; Owren, Brynjulf
1996
Condition numbers and their condition numbers. Zbl 0816.15004
Higham, Desmond J.
1995
Existence and stability of fixed points for a discretised nonlinear reaction-diffusion equation with delay. Zbl 0834.65079
Higham, Desmond J.; Sardar, Tasneem
1995
Equilibrium states of adaptive algorithms for delay differential equations. Zbl 0833.65070
Higham, Desmond J.; Famelis, Ioannis Th.
1995
The dynamics of a discretised nonlinear delay differential equation. Zbl 0797.65053
Higham, D. J.
1994
...and 19 more Documents
all top 5

### Cited by 2,941 Authors

 109 Jiang, Daqing 55 Mao, Xuerong 50 Higham, Desmond J. 40 Hayat, Tasawar 31 Liu, Meng 30 Liu, Qun 29 Al-saedi, Ahmed Eid Salem 26 Wang, Ke 25 Yuan, Chenggui 24 Zhang, Qimin 22 Gan, Siqing 22 Wu, Fuke 22 Yuan, Sanling 21 Wei, Yimin 20 Huang, Chengming 20 Reichel, Lothar 18 Estrada, Ernesto 16 D’Ambrosio, Raffaele 16 Ji, Chunyan 15 Buckwar, Evelyn 15 Diao, Huaian 15 Wang, Xiaojie 14 Jentzen, Arnulf 14 Liu, Mingzhu 14 Wang, Weiming 13 Burrage, Kevin 13 Kloeden, Peter Eris 13 Lv, Jingliang 13 Tocino, Alicia 13 Zou, Xiaoling 12 Li, Xiaoyue 12 Liu, Wei 12 Stoltz, Gabriel 12 Zhang, Xinhong 11 Arrigo, Francesca 11 Giles, Michael B. 11 Higham, Nicholas J. 11 Hong, Jialin 11 Kulikov, Gennady Yur’evich 11 O’Regan, Donal 11 Rathinasamy, Anandaraman 11 Song, Minghui 11 Teng, Zhi-dong 11 Zhang, Yunong 10 Deng, Feiqi 10 Szpruch, Lukasz 10 Xiao, Aiguo 9 Bao, Jianhai 9 Cai, Yongli 9 El Fatini, Mohamed 9 Jiang, Feng 9 Rodkina, Alexandra 9 Stuart, Andrew M. 9 Tan, Jianguo 9 Wei, Fengying 9 Zhang, Weihai 9 Zhang, Yan 9 Zhao, Dianli 9 Zhou, Baoquan 9 Zong, Xiaofeng 9 Zu, Li 8 Bou-Rabee, Nawaf M. 8 Feng, Tao 8 Guo, Qian 8 Hosseini, Seyed Mohammad 8 Hutzenthaler, Martin 8 Kühn, Christian 8 Luo, Xinlong 8 Qiu, Zhipeng 8 Sabanis, Sotirios 8 Senosiain, M. J. 8 Shi, Ningzhong 8 Zhang, Qiumei 8 Zhao, Yanan 7 Abdulle, Assyr 7 Benzi, Michele 7 Gao, Shujing 7 Guo, Yongfeng 7 Ho, Daniel W. C. 7 Khaliq, Abdul Q. M. 7 Neuenkirch, Andreas 7 Noferini, Vanni 7 Noschese, Silvia 7 Reisinger, Christoph 7 Rodriguez, Giuseppe 7 Tian, Hongjiong 7 Tudisco, Francesco 7 Vilmart, Gilles 7 Weiner, Rüdiger 7 Yue, Chao 7 Zhang, Tonghua 7 Zhao, Yu 7 Zhou, Shaobo 7 Zhu, Quanxin 6 Baker, Ruth Elizabeth 6 Cao, Wanrong 6 De la Cruz Cabrera, Omar 6 Ding, Xiaohua 6 Enright, Wayne H. 6 Han, Bingtao ...and 2,841 more Authors
all top 5

### Cited in 339 Serials

 187 Journal of Computational and Applied Mathematics 146 Applied Mathematics and Computation 74 Applied Numerical Mathematics 62 Advances in Difference Equations 51 BIT 49 Numerical Algorithms 48 Linear Algebra and its Applications 43 Physica A 42 International Journal of Computer Mathematics 41 Journal of Computational Physics 38 Abstract and Applied Analysis 35 Communications in Nonlinear Science and Numerical Simulation 31 Chaos, Solitons and Fractals 29 Journal of the Franklin Institute 29 SIAM Journal on Matrix Analysis and Applications 29 International Journal of Biomathematics 28 Discrete and Continuous Dynamical Systems. Series B 27 SIAM Journal on Scientific Computing 26 Computers & Mathematics with Applications 26 Journal of Applied Mathematics and Computing 25 Journal of Mathematical Analysis and Applications 25 Discrete Dynamics in Nature and Society 23 Mathematics and Computers in Simulation 23 Applied Mathematical Modelling 22 SIAM Journal on Numerical Analysis 21 Stochastic Analysis and Applications 19 Numerische Mathematik 19 Stochastic Processes and their Applications 19 Mathematical Problems in Engineering 19 Multiscale Modeling & Simulation 18 Automatica 16 Chaos 15 Journal of Difference Equations and Applications 14 Journal of Statistical Physics 13 Applied Mathematics Letters 13 Stochastics and Dynamics 12 Bulletin of Mathematical Biology 12 The Annals of Applied Probability 12 Journal of Nonlinear Science 12 Filomat 12 Nonlinear Dynamics 12 SIAM/ASA Journal on Uncertainty Quantification 11 Journal of Scientific Computing 10 Physica D 10 Advances in Computational Mathematics 10 Mathematical Biosciences and Engineering 10 Journal of Theoretical Biology 9 Mathematics of Computation 9 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 9 Computational and Applied Mathematics 9 Complexity 9 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 8 Mathematical Biosciences 8 Mathematical Methods in the Applied Sciences 8 Calcolo 8 Neural Computation 8 SIAM Review 8 Monte Carlo Methods and Applications 8 Methodology and Computing in Applied Probability 8 Journal of Applied Mathematics 8 Nonlinear Analysis. Hybrid Systems 8 Journal of Applied Analysis and Computation 8 International Journal of Systems Science. Principles and Applications of Systems and Integration 7 SIAM Journal on Applied Mathematics 7 Numerical Linear Algebra with Applications 7 Journal of Mathematical Chemistry 7 Statistics and Computing 6 International Journal of Control 6 Journal of Mathematical Physics 6 Systems & Control Letters 6 Statistics & Probability Letters 6 Mathematical and Computer Modelling 5 Journal of Mathematical Biology 5 Journal of Complexity 5 European Journal of Applied Mathematics 5 Journal of Computational Neuroscience 5 Bernoulli 5 International Journal of Theoretical and Applied Finance 5 Journal of Biological Systems 5 Qualitative Theory of Dynamical Systems 5 International Journal of Numerical Analysis and Modeling 5 Stochastics 5 Communications in Computational Physics 5 Discrete and Continuous Dynamical Systems. Series S 5 Journal of Computational Dynamics 5 AIMS Mathematics 5 SIAM Journal on Mathematics of Data Science 4 Applicable Analysis 4 Discrete Applied Mathematics 4 Journal of Fluid Mechanics 4 Nonlinearity 4 The Annals of Probability 4 Journal of Applied Probability 4 Numerical Methods for Partial Differential Equations 4 Japan Journal of Industrial and Applied Mathematics 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Random Operators and Stochastic Equations 4 Vietnam Journal of Mathematics 4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 Nonlinear Analysis. Real World Applications ...and 239 more Serials
all top 5

### Cited in 46 Fields

 1,125 Numerical analysis (65-XX) 1,102 Probability theory and stochastic processes (60-XX) 587 Ordinary differential equations (34-XX) 560 Biology and other natural sciences (92-XX) 199 Systems theory; control (93-XX) 155 Partial differential equations (35-XX) 155 Dynamical systems and ergodic theory (37-XX) 139 Linear and multilinear algebra; matrix theory (15-XX) 128 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 104 Combinatorics (05-XX) 100 Statistical mechanics, structure of matter (82-XX) 83 Computer science (68-XX) 76 Statistics (62-XX) 69 Operations research, mathematical programming (90-XX) 44 Fluid mechanics (76-XX) 33 Integral equations (45-XX) 27 Approximations and expansions (41-XX) 24 Calculus of variations and optimal control; optimization (49-XX) 21 Operator theory (47-XX) 19 Difference and functional equations (39-XX) 17 Mechanics of particles and systems (70-XX) 16 Mechanics of deformable solids (74-XX) 14 Quantum theory (81-XX) 13 Information and communication theory, circuits (94-XX) 12 Classical thermodynamics, heat transfer (80-XX) 12 Geophysics (86-XX) 8 Real functions (26-XX) 8 Optics, electromagnetic theory (78-XX) 5 Functional analysis (46-XX) 4 History and biography (01-XX) 4 Special functions (33-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Integral transforms, operational calculus (44-XX) 3 General and overarching topics; collections (00-XX) 3 Number theory (11-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Functions of a complex variable (30-XX) 2 Convex and discrete geometry (52-XX) 2 Relativity and gravitational theory (83-XX) 1 Mathematical logic and foundations (03-XX) 1 General algebraic systems (08-XX) 1 Field theory and polynomials (12-XX) 1 Measure and integration (28-XX) 1 Algebraic topology (55-XX) 1 Astronomy and astrophysics (85-XX)

### Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.