Edit Profile (opens in new tab) Higham, Desmond J. Co-Author Distance 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 · GND · IdRef Documents Indexed: 132 Publications since 1988, including 11 Books 1 Contribution as Editor · 1 Further Contribution Co-Authors: 63 Co-Authors with 96 Joint Publications 1,685 Co-Co-Authors all top 5 Co-Authors 33 single-authored 11 Mao, Xuerong 10 Grindrod, Peter 10 Higham, Nicholas J. 8 Arrigo, Francesca 8 Noferini, Vanni 7 Griffiths, David F. 6 Kalna, Gabriela 6 Stuart, Andrew M. 5 Anderson, David Frederick 4 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 3 Tudisco, Francesco 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 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 Di Giovacchino, Stefano 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 Gilmour, Craig 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 ...and 53 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 6 Multiscale Modeling & Simulation 5 Linear Algebra and its Applications 3 Numerische Mathematik 3 European Journal of Applied Mathematics 3 SIAM Journal on Scientific Computing 3 LMS Journal of Computation and Mathematics 3 Discrete and Continuous Dynamical Systems. Series B 3 Other Titles in Applied Mathematics 2 ACM Transactions on Mathematical Software 2 SIAM Journal on Scientific and Statistical Computing 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 SIAM Journal on Mathematics of Data Science 1 IMA Journal of Applied Mathematics 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 Pitman Research Notes in Mathematics Series 1 The Open Applied Mathematics Journal 1 SIAM/ASA Journal on Uncertainty Quantification 1 Springer Undergraduate Mathematics Series all top 5 Fields 95 Numerical analysis (65-XX) 42 Ordinary differential equations (34-XX) 39 Probability theory and stochastic processes (60-XX) 27 Combinatorics (05-XX) 22 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 20 Computer science (68-XX) 19 Biology and other natural sciences (92-XX) 10 Operations research, mathematical programming (90-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Statistics (62-XX) 4 Partial differential equations (35-XX) 2 General and overarching topics; collections (00-XX) 2 Systems theory; control (93-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 124 Publications have been cited 3,559 times in 2,629 Documents Cited by ▼ Year ▼ An algorithmic introduction to numerical simulation of stochastic differential equations. Zbl 0979.65007Higham, Desmond J. 982 2001 Strong convergence of Euler-type methods for nonlinear stochastic differential equations. Zbl 1026.65003Higham, Desmond J.; Mao, Xuerong; Stuart, Andrew M. 331 2002 Riemann manifold Langevin and Hamiltonian Monte Carlo methods. With discussion and authors’ reply. Zbl 1411.62071Girolami, Mark; Calderhead, Ben 226 2011 Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise. Zbl 1075.60072Mattingly, J. C.; Stuart, A. M.; Higham, D. J. 221 2002 Mean-square and asymptotic stability of the stochastic theta method. Zbl 0982.60051Higham, Desmond J. 197 2000 Numerical methods for nonlinear stochastic differential equations with jumps. Zbl 1186.65010Higham, Desmond J.; Kloeden, Peter. E. 122 2005 Network properties revealed through matrix functions. Zbl 1214.05077Estrada, Ernesto; Higham, Desmond J. 106 2010 Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations. Zbl 1144.65005Higham, Desmond J.; Mao, Xuerong; Yuan, Chenggui 105 2007 Exponential mean-square stability of numerical solutions to stochastic differential equations. Zbl 1055.65009Higham, Desmond J.; Mao, Xuerong; Stuart, Andrew M. 83 2003 Convergence and stability of implicit methods for jump-diffusion systems. Zbl 1109.65007Higham, Desmond J.; Kloeden, Peter E. 63 2006 Numerical methods for ordinary differential equations. Initial value problems. Zbl 1209.65070Griffiths, David F.; Higham, Desmond J. 62 2010 Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems. Zbl 1128.65007Higham, Desmond J.; Kloeden, Peter E. 57 2007 \(A\)-stability and stochastic mean-square stability. Zbl 0961.65003Higham, Desmond J. 51 2000 Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model. Zbl 1230.65011Szpruch, Lukasz; Mao, Xuerong; Higham, Desmond J.; Pan, Jiazhu 51 2011 Structured backward error and condition of generalized eigenvalue problems. Zbl 0935.65032Higham, Desmond J.; Higham, Nicholas J. 50 1998 Multilevel Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics. Zbl 1262.60072Anderson, David F.; Higham, Desmond J. 44 2012 Backward error and condition of structured linear systems. Zbl 0747.65028Higham, Desmond J.; Higham, Nicholas J. 43 1992 Convergence, nonnegativity and stability of a new Milstein scheme with applications to finance. Zbl 1279.60068Higham, Desmond J.; Mao, Xuerong; Szpruch, Lukasz 42 2013 Modeling and simulating chemical reactions. Zbl 1144.80011Higham, Desmond J. 42 2008 Numerical simulation of a linear stochastic oscillator with additive noise. Zbl 1060.65007Strømmen Melbø, Aslaug H.; Higham, Desmond J. 38 2004 Condition numbers and their condition numbers. Zbl 0816.15004Higham, Desmond J. 35 1995 Deep learning: an introduction for applied mathematicians. Zbl 1440.68214Higham, Catherine F.; Higham, Desmond J. 28 2019 An introduction to financial option valuation. Mathematics, stochastics and computation. Zbl 1122.91001Higham, Desmond J. 28 2004 Trust region algorithms and timestep selection. Zbl 0945.65068Higham, Desmond J. 27 1999 Stiffness of ODEs. Zbl 0782.65091Higham, Desmond J.; Trefethen, Lloyd N. 27 1993 Analyzing multi-level Monte Carlo for options with non-globally Lipschitz payoff. Zbl 1199.65008Giles, Michael B.; Higham, Desmond J.; Mao, Xuerong 26 2009 Existence and stability of fixed points for a discretised nonlinear reaction-diffusion equation with delay. Zbl 0834.65079Higham, Desmond J.; Sardar, Tasneem 25 1995 Stochastic ordinary differential equations in applied and computational mathematics. Zbl 1221.60099Higham, Desmond J. 23 2011 Global error versus tolerance for explicit Runge-Kutta methods. Zbl 0738.65073Higham, Desmond J. 20 1991 Large growth factors in Gaussian elimination with pivoting. Zbl 0681.65012Higham, Nicholas J.; Higham, Desmond J. 20 1989 Matlab guide. 2nd ed. Zbl 1067.68180Higham, Desmond J; Higham, Nicholas J. 20 2005 On the boundedness of asymptotic stability regions for the stochastic theta method. Zbl 1026.65004Bryden, Alan; Higham, Desmond J. 19 2003 Preserving exponential mean-square stability in the simulation of hybrid stochastic differential equations. Zbl 1137.65007Higham, Desmond J.; Mao, Xuerong; Yuan, Chenggui 19 2007 Asymptotic stability of a jump-diffusion equation and its numerical approximation. Zbl 1190.65010Chalmers, Graeme D.; Higham, Desmond J. 18 2008 Complexity of multilevel Monte Carlo tau-leaping. Zbl 1327.60136Anderson, David F.; Higham, Desmond J.; Sun, Yu 17 2014 Componentwise perturbation theory for linear systems with multiple right- hand sides. Zbl 0801.65043Higham, Desmond J.; Higham, Nicholas J. 16 1992 Stepsize selection for tolerance proportionality in explicit Runge-Kutta codes. Zbl 0891.65097Calvo, M.; Higham, D. J.; Montijano, J. I.; Rández, L. 15 1997 Analysis of stepsize selection schemes for Runge-Kutta codes. Zbl 0661.65077Hall, G.; Higham, D. J. 14 1988 Robust defect control with Runge-Kutta schemes. Zbl 0682.65033Higham, Desmond J. 14 1989 Mean exit times and the multilevel Monte Carlo method. Zbl 1282.65020Higham, Desmond J.; Mao, Xuerong; Roj, Mikolaj; Song, Qingshuo; Yin, George 13 2013 A dynamical systems view of network centrality. Zbl 1371.90039Grindrod, Peter; Higham, Desmond J. 13 2014 Convergence and stability analysis for implicit simulations of stochastic differential equations with random jump magnitudes. Zbl 1148.65005Chalmers, Graeme D.; Higham, Desmond J. 13 2008 Betweenness in time dependent networks. Zbl 1352.90020Alsayed, Ahmad; Higham, Desmond J. 13 2015 Parallel defect control. Zbl 0743.65069Enright, W. H.; Higham, D. J. 12 1991 A matrix iteration for dynamic network summaries. Zbl 1262.91121Grindrod, Peter; Higham, Desmond J. 12 2013 The tolerance proportionality of adaptive ODE solvers. Zbl 0780.65050Higham, Desmond J. 12 1993 The deformed graph Laplacian and its applications to network centrality analysis. Zbl 1381.05043Grindrod, Peter; Higham, Desmond J.; Noferini, Vanni 11 2018 Runge-Kutta defect control using Hermite-Birkhoff interpolation. Zbl 0745.65051Higham, Desmond J. 11 1991 Matlab guide. Zbl 0953.68642Higham, Desmond J.; Higham, Nicholas J. 11 2000 Spectral clustering and its use in bioinformatics. Zbl 1123.65024Higham, Desmond J.; Kalna, Gabriela; Kibble, Milla 11 2007 Nonnormality and stochastic differential equations. Zbl 1105.65007Higham, D. J.; Mao, X. 11 2006 Comparing hitting time behavior of Markov jump processes and their diffusion approximations. Zbl 1202.60138Szpruch, Lukasz; Higham, Desmond J. 10 2010 Runge-Kutta type methods for orthogonal integration. Zbl 0866.65047Higham, Desmond J. 10 1996 Time-stepping and preserving orthonormality. Zbl 0891.65082Higham, Desmond J. 10 1997 Mapping directed networks. Zbl 1205.65166Crofts, Jonathan J.; Estrada, Ernesto; Higham, Desmond J.; Taylor, Alan 10 2010 Analysis of the Enright-Kamel partitioning method for stiff ordinary differential equations. Zbl 0659.65069Higham, Desmond J. 9 1989 Network science. Complexity in nature and technology. Zbl 1202.68024 9 2010 Multilevel Monte Carlo for stochastic differential equations with small noise. Zbl 1334.60128Anderson, David F.; Higham, Desmond J.; Sun, Yu 9 2016 First and second moment reversion for a discretized square root process with jumps. Zbl 1188.91241Chalmers, Graeme D.; Higham, Desmond J. 9 2010 On the exponential generating function for non-backtracking walks. Zbl 1394.05119Arrigo, Francesca; Grindrod, Peter; Higham, Desmond J.; Noferini, Vanni 8 2018 Evolving graphs: dynamical models, inverse problems and propagation. Zbl 1195.05075Grindrod, Peter; Higham, Desmond J. 8 2010 Global error estimation with adaptive explicit Runge-Kutta methods. Zbl 0840.65087Calvo, M.; Higham, D. J.; Montijano, J. I.; Rández, L. 8 1996 A nonlinear spectral method for core-periphery detection in networks. Zbl 1499.05402Tudisco, Francesco; Higham, Desmond J. 8 2019 Nine ways to implement the binomial method for option valuation in MATLAB. Zbl 1029.91030Higham, Desmond J. 8 2002 Matlab guide. 3rd revised and updated edition. Zbl 1357.68001Higham, Desmond J; Higham, Nicholas J. 8 2017 An introduction to the numerical simulation of stochastic differential equations. Zbl 07335009Higham, Desmond J.; Kloeden, Peter E. 8 2021 On constrained Langevin equations and (bio)chemical reaction networks. Zbl 1481.60146Anderson, David F.; Higham, Desmond J.; Leite, Saul C.; Williams, Ruth J. 7 2019 Dynamics of constant and variable stepsize methods for a nonlinear population model with delay. Zbl 0899.92027Sardar, Tasneem K.; Higham, Desmond J. 7 1997 Does error control suppress spuriosity? Zbl 0873.65083Aves, Mark A.; Griffiths, David F.; Higham, Desmond J. 7 1997 Highly continuous Runge-Kutta interpolants. Zbl 0900.65235Higham, D. J. 7 1991 Non-backtracking walk centrality for directed networks. Zbl 1460.90040Arrigo, Francesca; Grindrod, Peter; Higham, Desmond J.; Noferini, Vanni 7 2018 Embedded Runge-Kutta formulae with stable equilibrium states. Zbl 0704.65054Higham, D. J.; Hall, G. 5 1990 Monotonic piecewise cubic interpolation, with applications to ODE plotting. Zbl 0768.65002Higham, D. J. 5 1992 A matrix perturbation view of the small world phenomenon. Zbl 1050.65004Higham, Desmond J. 5 2003 Block matrix formulations for evolving networks. Zbl 1362.05120Fenu, Caterina; Higham, Desmond J. 5 2017 Discovering bipartite substructure in directed networks. Zbl 1223.68087Taylor, Alan; Vass, J. Keith; Higham, Desmond J. 5 2011 A clustering coefficient for weighted networks, with application to gene expression data. Zbl 1189.68084Kalna, Gabriela; Higham, Desmond J. 5 2007 A framework for second-order eigenvector centralities and clustering coefficients. Zbl 1472.65043Arrigo, Francesca; Higham, Desmond J.; Tudisco, Francesco 5 2020 Computational complexity analysis for Monte Carlo approximations of classically scaled population processes. Zbl 1401.60130Anderson, David F.; Higham, Desmond J.; Sun, Yu 4 2018 Non-backtracking alternating walks. Zbl 1422.05061Arrigo, Francesca; Higham, Desmond J.; Noferini, Vanni 4 2019 Non-backtracking PageRank. Zbl 1425.65046Arrigo, Francesca; Higham, Desmond J.; Noferini, Vanni 4 2019 The structured sensitivity of Vandermonde-like systems. Zbl 0766.65042Bartels, Sven G.; Higham, Desmond J. 4 1992 Googling the brain: discovering hierarchical and asymmetric network structures, with applications in neuroscience. Zbl 1245.05118Crofts, Jonathan J.; Higham, Desmond J. 4 2011 Core-periphery detection in hypergraphs. Zbl 1515.65081Tudisco, Francesco; Higham, Desmond J. 4 2023 Analysis of the dynamics of local error control via a piecewise continuous residual. Zbl 0907.65077Higham, D. J.; Stuart, A. M. 4 1998 Unravelling small world networks. Zbl 1028.65034Higham, Desmond J. 4 2003 A matrix perturbation view of the small world phenomenon. Zbl 1119.65008Higham, Desmond J. 4 2007 Beyond non-backtracking: non-cycling network centrality measures. Zbl 1472.05081Arrigo, Francesca; Higham, Desmond J.; Noferini, Vanni 4 2020 Random matrices generating large growth in LU factorization with pivoting. Zbl 1459.65036Higham, Desmond J.; Higham, Nicholas J.; Pranesh, Srikara 4 2021 Defect estimation in Adams PECE codes. Zbl 0676.65082Higham, Desmond J. 3 1989 Bistability through triadic closure. Zbl 1258.05115Grindrod, Peter; Higham, Desmond J.; Parsons, Mark C. 3 2012 An introduction to multilevel Monte Carlo for option valuation. Zbl 1335.91102Higham, Desmond J. 3 2015 Centrality analysis for modified lattices. Zbl 1373.05186Paton, Martin; Akartunali, Kerem; Higham, Desmond J. 3 2017 Error analysis of QR algorithms for computing Lyapunov exponents. Zbl 1022.65079McDonald, Edward J.; Higham, Desmond J. 3 2001 Greedy pathlengths and small world graphs. Zbl 1095.68083Higham, Desmond J. 3 2006 Equilibrium states of adaptive algorithms for delay differential equations. Zbl 0833.65070Higham, Desmond J.; Famelis, Ioannis Th. 3 1995 Analysis of the singular value decomposition as a tool for processing microarray expression data. Zbl 1183.68533Higham, Desmond J.; Kalna, Gabriela; Vass, J. Keith 3 2005 Regular Runge-Kutta pairs. Zbl 0890.65076Higham, Desmond J. 3 1997 Switching and diffusion models for gene regulation networks. Zbl 1184.92016Intep, Somkid; Higham, Desmond J.; Mao, Xuerong 3 2009 Chemical master equation and Langevin regimes for a gene transcription model. Zbl 1151.92012Khanin, Raya; Higham, Desmond J. 3 2008 Core-periphery detection in hypergraphs. Zbl 1515.65081Tudisco, Francesco; Higham, Desmond J. 4 2023 An introduction to the numerical simulation of stochastic differential equations. Zbl 07335009Higham, Desmond J.; Kloeden, Peter E. 8 2021 Random matrices generating large growth in LU factorization with pivoting. Zbl 1459.65036Higham, Desmond J.; Higham, Nicholas J.; Pranesh, Srikara 4 2021 Accurately computing the log-sum-exp and softmax functions. Zbl 1509.65019Blanchard, Pierre; Higham, Desmond J.; Higham, Nicholas J. 2 2021 A framework for second-order eigenvector centralities and clustering coefficients. Zbl 1472.65043Arrigo, Francesca; Higham, Desmond J.; Tudisco, Francesco 5 2020 Beyond non-backtracking: non-cycling network centrality measures. Zbl 1472.05081Arrigo, Francesca; Higham, Desmond J.; Noferini, Vanni 4 2020 A network model for polarization of political opinion. Zbl 1437.91346Higham, Desmond J.; Mantzaris, Alexander V. 1 2020 Deep learning: an introduction for applied mathematicians. Zbl 1440.68214Higham, Catherine F.; Higham, Desmond J. 28 2019 A nonlinear spectral method for core-periphery detection in networks. Zbl 1499.05402Tudisco, Francesco; Higham, Desmond J. 8 2019 On constrained Langevin equations and (bio)chemical reaction networks. Zbl 1481.60146Anderson, David F.; Higham, Desmond J.; Leite, Saul C.; Williams, Ruth J. 7 2019 Non-backtracking alternating walks. Zbl 1422.05061Arrigo, Francesca; Higham, Desmond J.; Noferini, Vanni 4 2019 Non-backtracking PageRank. Zbl 1425.65046Arrigo, Francesca; Higham, Desmond J.; Noferini, Vanni 4 2019 Centrality-friendship paradoxes: when our friends are more important than us. Zbl 1472.05038Higham, Desmond J. 1 2019 The deformed graph Laplacian and its applications to network centrality analysis. Zbl 1381.05043Grindrod, Peter; Higham, Desmond J.; Noferini, Vanni 11 2018 On the exponential generating function for non-backtracking walks. Zbl 1394.05119Arrigo, Francesca; Grindrod, Peter; Higham, Desmond J.; Noferini, Vanni 8 2018 Non-backtracking walk centrality for directed networks. Zbl 1460.90040Arrigo, Francesca; Grindrod, Peter; Higham, Desmond J.; Noferini, Vanni 7 2018 Computational complexity analysis for Monte Carlo approximations of classically scaled population processes. Zbl 1401.60130Anderson, David F.; Higham, Desmond J.; Sun, Yu 4 2018 Matlab guide. 3rd revised and updated edition. Zbl 1357.68001Higham, Desmond J; Higham, Nicholas J. 8 2017 Block matrix formulations for evolving networks. Zbl 1362.05120Fenu, Caterina; Higham, Desmond J. 5 2017 Centrality analysis for modified lattices. Zbl 1373.05186Paton, Martin; Akartunali, Kerem; Higham, Desmond J. 3 2017 Multilevel Monte Carlo for stochastic differential equations with small noise. Zbl 1334.60128Anderson, David F.; Higham, Desmond J.; Sun, Yu 9 2016 Inverse network sampling to explore online brand allegiance. Zbl 1408.91177Grindrod, Peter; Higham, Desmond J.; Laflin, Peter; Otley, Amanda; Ward, Jonathan A. 1 2016 Betweenness in time dependent networks. Zbl 1352.90020Alsayed, Ahmad; Higham, Desmond J. 13 2015 An introduction to multilevel Monte Carlo for option valuation. Zbl 1335.91102Higham, Desmond J. 3 2015 Complexity of multilevel Monte Carlo tau-leaping. Zbl 1327.60136Anderson, David F.; Higham, Desmond J.; Sun, Yu 17 2014 A dynamical systems view of network centrality. Zbl 1371.90039Grindrod, Peter; Higham, Desmond J. 13 2014 Convergence, nonnegativity and stability of a new Milstein scheme with applications to finance. Zbl 1279.60068Higham, Desmond J.; Mao, Xuerong; Szpruch, Lukasz 42 2013 Mean exit times and the multilevel Monte Carlo method. Zbl 1282.65020Higham, Desmond J.; Mao, Xuerong; Roj, Mikolaj; Song, Qingshuo; Yin, George 13 2013 A matrix iteration for dynamic network summaries. Zbl 1262.91121Grindrod, Peter; Higham, Desmond J. 12 2013 Multilevel Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics. Zbl 1262.60072Anderson, David F.; Higham, Desmond J. 44 2012 Bistability through triadic closure. Zbl 1258.05115Grindrod, Peter; Higham, Desmond J.; Parsons, Mark C. 3 2012 Models for evolving networks: with applications in telecommunication and online activities. Zbl 1248.90032Grindrod, Peter; Higham, Desmond J. 2 2012 A model for dynamic communicators. Zbl 1254.91699Mantzaris, Alexander V.; Higham, Desmond J. 1 2012 Riemann manifold Langevin and Hamiltonian Monte Carlo methods. With discussion and authors’ reply. Zbl 1411.62071Girolami, Mark; Calderhead, Ben 226 2011 Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model. Zbl 1230.65011Szpruch, Lukasz; Mao, Xuerong; Higham, Desmond J.; Pan, Jiazhu 51 2011 Stochastic ordinary differential equations in applied and computational mathematics. Zbl 1221.60099Higham, Desmond J. 23 2011 Discovering bipartite substructure in directed networks. Zbl 1223.68087Taylor, Alan; Vass, J. Keith; Higham, Desmond J. 5 2011 Googling the brain: discovering hierarchical and asymmetric network structures, with applications in neuroscience. Zbl 1245.05118Crofts, Jonathan J.; Higham, Desmond J. 4 2011 Hybrid simulation of autoregulation within transcription and translation. Zbl 1211.92020Higham, Desmond J.; Intep, Somkid; Mao, Xuerong; Szpruch, Lukasz 1 2011 Network properties revealed through matrix functions. Zbl 1214.05077Estrada, Ernesto; Higham, Desmond J. 106 2010 Numerical methods for ordinary differential equations. Initial value problems. Zbl 1209.65070Griffiths, David F.; Higham, Desmond J. 62 2010 Comparing hitting time behavior of Markov jump processes and their diffusion approximations. Zbl 1202.60138Szpruch, Lukasz; Higham, Desmond J. 10 2010 Mapping directed networks. Zbl 1205.65166Crofts, Jonathan J.; Estrada, Ernesto; Higham, Desmond J.; Taylor, Alan 10 2010 Network science. Complexity in nature and technology. Zbl 1202.68024 9 2010 First and second moment reversion for a discretized square root process with jumps. Zbl 1188.91241Chalmers, Graeme D.; Higham, Desmond J. 9 2010 Evolving graphs: dynamical models, inverse problems and propagation. Zbl 1195.05075Grindrod, Peter; Higham, Desmond J. 8 2010 Zero, one and two-switch models of gene regulation. Zbl 1201.37114Intep, Somkid; Higham, Desmond J. 2 2010 Analyzing multi-level Monte Carlo for options with non-globally Lipschitz payoff. Zbl 1199.65008Giles, Michael B.; Higham, Desmond J.; Mao, Xuerong 26 2009 Switching and diffusion models for gene regulation networks. Zbl 1184.92016Intep, Somkid; Higham, Desmond J.; Mao, Xuerong 3 2009 Modeling and simulating chemical reactions. Zbl 1144.80011Higham, Desmond J. 42 2008 Asymptotic stability of a jump-diffusion equation and its numerical approximation. Zbl 1190.65010Chalmers, Graeme D.; Higham, Desmond J. 18 2008 Convergence and stability analysis for implicit simulations of stochastic differential equations with random jump magnitudes. Zbl 1148.65005Chalmers, Graeme D.; Higham, Desmond J. 13 2008 Chemical master equation and Langevin regimes for a gene transcription model. Zbl 1151.92012Khanin, Raya; Higham, Desmond J. 3 2008 Chemical master versus chemical Langevin for first-order reaction networks. Zbl 1322.92089Higham, Desmond J.; Khanin, Raya 2 2008 Multidimensional partitioning and bi-partitioning: Analysis and application to gene expression data sets. Zbl 1138.65029Kalna, Gabriela; Vass, J. Keith; Higham, Desmond J. 1 2008 Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations. Zbl 1144.65005Higham, Desmond J.; Mao, Xuerong; Yuan, Chenggui 105 2007 Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems. Zbl 1128.65007Higham, Desmond J.; Kloeden, Peter E. 57 2007 Preserving exponential mean-square stability in the simulation of hybrid stochastic differential equations. Zbl 1137.65007Higham, Desmond J.; Mao, Xuerong; Yuan, Chenggui 19 2007 Spectral clustering and its use in bioinformatics. Zbl 1123.65024Higham, Desmond J.; Kalna, Gabriela; Kibble, Milla 11 2007 A clustering coefficient for weighted networks, with application to gene expression data. Zbl 1189.68084Kalna, Gabriela; Higham, Desmond J. 5 2007 A matrix perturbation view of the small world phenomenon. Zbl 1119.65008Higham, Desmond J. 4 2007 Spectral analysis of two-signed microarray expression data. Zbl 1148.92016Higham, Desmond J.; Kalna, Gabriela; Vass, J. Keith 2 2007 Convergence and stability of implicit methods for jump-diffusion systems. Zbl 1109.65007Higham, Desmond J.; Kloeden, Peter E. 63 2006 Nonnormality and stochastic differential equations. Zbl 1105.65007Higham, D. J.; Mao, X. 11 2006 Greedy pathlengths and small world graphs. Zbl 1095.68083Higham, Desmond J. 3 2006 Numerical methods for nonlinear stochastic differential equations with jumps. Zbl 1186.65010Higham, Desmond J.; Kloeden, Peter. E. 122 2005 Matlab guide. 2nd ed. Zbl 1067.68180Higham, Desmond J; Higham, Nicholas J. 20 2005 Analysis of the singular value decomposition as a tool for processing microarray expression data. Zbl 1183.68533Higham, Desmond J.; Kalna, Gabriela; Vass, J. Keith 3 2005 Google PageRank as mean playing time for pinball on the reverse web. Zbl 1083.68509Higham, Desmond J. 2 2005 Spectral reordering of a range-dependent weighted random graph. Zbl 1077.92001Higham, Desmond J. 1 2005 Numerical simulation of a linear stochastic oscillator with additive noise. Zbl 1060.65007Strømmen Melbø, Aslaug H.; Higham, Desmond J. 38 2004 An introduction to financial option valuation. Mathematics, stochastics and computation. Zbl 1122.91001Higham, Desmond J. 28 2004 An introduction to financial option valuation. Mathematics, stochastics and computation. Zbl 1140.91003Higham, Desmond J. 1 2004 Exponential mean-square stability of numerical solutions to stochastic differential equations. Zbl 1055.65009Higham, Desmond J.; Mao, Xuerong; Stuart, Andrew M. 83 2003 On the boundedness of asymptotic stability regions for the stochastic theta method. Zbl 1026.65004Bryden, Alan; Higham, Desmond J. 19 2003 A matrix perturbation view of the small world phenomenon. Zbl 1050.65004Higham, Desmond J. 5 2003 Unravelling small world networks. Zbl 1028.65034Higham, Desmond J. 4 2003 Strong convergence of Euler-type methods for nonlinear stochastic differential equations. Zbl 1026.65003Higham, Desmond J.; Mao, Xuerong; Stuart, Andrew M. 331 2002 Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise. Zbl 1075.60072Mattingly, J. C.; Stuart, A. M.; Higham, D. J. 221 2002 Nine ways to implement the binomial method for option valuation in MATLAB. Zbl 1029.91030Higham, Desmond J. 8 2002 An algorithmic introduction to numerical simulation of stochastic differential equations. Zbl 0979.65007Higham, Desmond J. 982 2001 Error analysis of QR algorithms for computing Lyapunov exponents. Zbl 1022.65079McDonald, Edward J.; Higham, Desmond J. 3 2001 Mean-square and asymptotic stability of the stochastic theta method. Zbl 0982.60051Higham, Desmond J. 197 2000 \(A\)-stability and stochastic mean-square stability. Zbl 0961.65003Higham, Desmond J. 51 2000 Matlab guide. Zbl 0953.68642Higham, Desmond J.; Higham, Nicholas J. 11 2000 The effect of quadrature on the dynamics of a discretized nonlinear integro-differential equation. Zbl 0946.65136Aves, Mark A.; Davies, Penny J.; Higham, Desmond J. 2 2000 Phase space error control for dynamical systems. Zbl 0963.65140Higham, D. J.; Humphries, A. R.; Wain, R. J. 2 2000 Runge-Kutta solutions of a hyperbolic conservation law with source term. Zbl 0966.65063Aves, Mark A.; Griffiths, David F.; Higham, Desmond J. 2 2000 Theta method dynamics. Zbl 0953.65054Barclay, Graeme J.; Griffiths, David F.; Higham, Desmond J. 1 2000 Trust region algorithms and timestep selection. Zbl 0945.65068Higham, Desmond J. 27 1999 Qualitative properties of modified equations. Zbl 0935.34003Gonzalez, O.; Higham, D. J.; Stuart, A. M. 2 1999 Structured backward error and condition of generalized eigenvalue problems. Zbl 0935.65032Higham, Desmond J.; Higham, Nicholas J. 50 1998 Analysis of the dynamics of local error control via a piecewise continuous residual. Zbl 0907.65077Higham, D. J.; Stuart, A. M. 4 1998 Stepsize selection for tolerance proportionality in explicit Runge-Kutta codes. Zbl 0891.65097Calvo, M.; Higham, D. J.; Montijano, J. I.; Rández, L. 15 1997 Time-stepping and preserving orthonormality. Zbl 0891.65082Higham, Desmond J. 10 1997 Dynamics of constant and variable stepsize methods for a nonlinear population model with delay. Zbl 0899.92027Sardar, Tasneem K.; Higham, Desmond J. 7 1997 Does error control suppress spuriosity? Zbl 0873.65083Aves, Mark A.; Griffiths, David F.; Higham, Desmond J. 7 1997 Regular Runge-Kutta pairs. Zbl 0890.65076Higham, Desmond J. 3 1997 Runge-Kutta type methods for orthogonal integration. Zbl 0866.65047Higham, Desmond J. 10 1996 Global error estimation with adaptive explicit Runge-Kutta methods. Zbl 0840.65087Calvo, M.; Higham, D. J.; Montijano, J. I.; Rández, L. 8 1996 ...and 24 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,500 Authors 141 Jiang, Daqing 64 Mao, Xuerong 50 Higham, Desmond J. 46 Hayat, Tasawar 42 Liu, Qun 33 Al-saedi, Ahmed Eid Salem 33 Liu, Meng 32 Zhang, Qimin 29 Wang, Ke 26 Yuan, Chenggui 25 Gan, Siqing 25 Wu, Fuke 25 Yuan, Sanling 21 D’Ambrosio, Raffaele 21 Huang, Chengming 21 Wei, Yimin 20 Reichel, Lothar 19 Estrada, Ernesto 19 Ji, Chunyan 19 Liu, Wei 18 Teng, Zhi-dong 18 Wang, Weiming 17 Lv, Jingliang 17 Wang, Xiaojie 17 Zhang, Xinhong 17 Zou, Xiaoling 16 Buckwar, Evelyn 15 Diao, Huaian 15 Liu, Mingzhu 15 Stoltz, Gabriel 14 Jentzen, Arnulf 14 Kulikov, Gennady Yur’evich 13 Burrage, Kevin 13 Cai, Yongli 13 Kloeden, Peter Eris 13 Li, Xiaoyue 13 Rathinasamy, Anandaraman 13 Xiao, Aiguo 12 Ahmad, Bashir 12 Arrigo, Francesca 12 Higham, Nicholas J. 12 Hong, Jialin 12 O’Regan, Donal 12 Song, Minghui 12 Wei, Chunjin 12 Wei, Fengying 12 Zhang, Yunong 12 Zhou, Baoquan 12 Zhu, Quanxin 11 Bao, Jianhai 11 El Fatini, Mohamed 11 Giles, Michael B. 11 Zhang, Tonghua 10 Abdulle, Assyr 10 Bou-Rabee, Nawaf M. 10 Deng, Feiqi 10 Feng, Tao 10 Guo, Qian 10 Luo, Xinlong 10 Shi, Ningzhong 10 Stuart, Andrew M. 10 Szpruch, Lukasz 10 Tudisco, Francesco 10 Zhang, Yan 10 Zong, Xiaofeng 9 Di Giovacchino, Stefano 9 Gao, Shujing 9 Jiang, Feng 9 Noferini, Vanni 9 Qiu, Zhipeng 9 Rodkina, Alexandra 9 Senosiain, M. J. 9 Shen, Yi 9 Shi, Zhenfeng 9 Tan, Jianguo 9 Wang, Yan 9 Zhang, Qiumei 9 Zhang, Wei 9 Zhang, Weihai 9 Zhao, Dianli 9 Zu, Li 8 Cai, Yongmei 8 Han, Bingtao 8 Hosseini, Seyed Mohammad 8 Hu, Junhao 8 Hutzenthaler, Martin 8 Kressner, Daniel 8 Kühn, Christian 8 Neuenkirch, Andreas 8 Noschese, Silvia 8 Pavliotis, Grigorios A. 8 Przybyłowicz, Paweł 8 Sabanis, Sotirios 8 Schütte, Christof 8 Schweitzer, Marcel 8 Sun, Shulin 8 Wang, Kai 8 Zhang, Shuwen 8 Zhao, Yanan 8 Zhao, Yu ...and 3,400 more Authors all top 5 Cited in 375 Serials 198 Journal of Computational and Applied Mathematics 157 Applied Mathematics and Computation 90 Physica A 88 Applied Numerical Mathematics 67 Advances in Difference Equations 54 Journal of Computational Physics 54 BIT 54 Numerical Algorithms 52 Linear Algebra and its Applications 50 Communications in Nonlinear Science and Numerical Simulation 46 International Journal of Computer Mathematics 38 Chaos, Solitons and Fractals 38 Abstract and Applied Analysis 35 Journal of the Franklin Institute 34 SIAM Journal on Matrix Analysis and Applications 34 Discrete and Continuous Dynamical Systems. 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Principles and Applications of Systems and Integration 7 International Journal of Control 7 Journal of Fluid Mechanics 7 Statistics & Probability Letters 7 Numerical Linear Algebra with Applications 7 Journal of Computational Neuroscience 7 Bernoulli 7 Journal of Mathematical Chemistry 7 Journal of Biological Dynamics 7 Journal of Physics A: Mathematical and Theoretical 6 Journal of Mathematical Biology 6 Journal of Differential Equations 6 Mathematical and Computer Modelling 6 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 6 SIAM Journal on Applied Dynamical Systems 6 Acta Numerica 6 Journal of Statistical Mechanics: Theory and Experiment 6 Communications in Computational Physics 6 Discrete and Continuous Dynamical Systems. Series S 6 Journal of Computational Dynamics 5 Applicable Analysis 5 Nonlinearity 5 Journal of Applied Probability 5 Journal of Complexity 5 Numerical Methods for Partial Differential Equations 5 European Journal of Applied Mathematics 5 Japan Journal of Industrial and Applied Mathematics 5 International Journal of Theoretical and Applied Finance 5 Qualitative Theory of Dynamical Systems 5 International Journal of Nonlinear Sciences and Numerical Simulation 5 Journal of Systems Science and Complexity 5 International Journal of Numerical Analysis and Modeling ...and 275 more Serials all top 5 Cited in 47 Fields 1,351 Probability theory and stochastic processes (60-XX) 1,279 Numerical analysis (65-XX) 739 Biology and other natural sciences (92-XX) 692 Ordinary differential equations (34-XX) 224 Systems theory; control (93-XX) 202 Partial differential equations (35-XX) 178 Dynamical systems and ergodic theory (37-XX) 158 Linear and multilinear algebra; matrix theory (15-XX) 145 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 133 Statistical mechanics, structure of matter (82-XX) 123 Combinatorics (05-XX) 105 Computer science (68-XX) 95 Statistics (62-XX) 89 Operations research, mathematical programming (90-XX) 55 Fluid mechanics (76-XX) 37 Integral equations (45-XX) 29 Calculus of variations and optimal control; optimization (49-XX) 27 Approximations and expansions (41-XX) 26 Operator theory (47-XX) 22 Difference and functional equations (39-XX) 18 Mechanics of particles and systems (70-XX) 17 Mechanics of deformable solids (74-XX) 17 Geophysics (86-XX) 16 Quantum theory (81-XX) 16 Information and communication theory, circuits (94-XX) 15 Classical thermodynamics, heat transfer (80-XX) 9 Real functions (26-XX) 8 Optics, electromagnetic theory (78-XX) 6 Functional analysis (46-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 General and overarching topics; collections (00-XX) 4 History and biography (01-XX) 4 Number theory (11-XX) 4 Special functions (33-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Integral transforms, operational calculus (44-XX) 3 Astronomy and astrophysics (85-XX) 2 Functions of a complex variable (30-XX) 2 Convex and discrete geometry (52-XX) 2 Relativity and gravitational theory (83-XX) 1 Order, lattices, ordered algebraic structures (06-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 Manifolds and cell complexes (57-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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