Publications

Manuscript

BM Herbst and Bengt Fornberg. Modeling in Applied Mathematics. (2010)

Journal & Conference

  • B.M Herbst. Collocation methods and the solution of conduction-convection problems. Int. J. Numer. Meth. Engng., 17, pp1093-1102 (1981).
  • B.M. Herbst and J.F. Botha. Computable error estimates for the collocation method applied to two-point boundary value problems. IMA J. Numer. Anal., 1, pp489-497 (1982).
  • B.M Herbst, S.W. Schoombie and A.R. Mitchell. A moving Petrov-Galerkin method for transport equations. Int. J. Numer. Meth. Engng., 18, pp1321-1336 (1983).
  • B.M Herbst, S.W. Schoombie and A.R. Mitchell. Equidistributing principles in moving finite element methods. J. Comput. Appl. Math., 9, pp377-389 (1983).
  • B.M Herbst, S.W. Schoombie, A.R. Mitchell and D.F.~Griffiths. Generalised Petrov-Galerkin methods for the numerical solution of Burgers’ equation. Int. J. Numer. Meth. Engng., 20, pp1273-1290 (1984).
  • B.M. Herbst. On upwind collocation methods. Comm. Appl. Numer. Meth., 1, pp97-100 (1985).
  • B.M Herbst, A.R. Mitchell and J.A.C. Weideman. On the stability of the nonlinear Schr”odinger equation. J. Comput. Phys., 60, pp263-281 (1985).
  • B.M. Herbst, J.Ll. Morris and A.R. Mitchell. Numerical experience with the nonlinear Schr”odinger equation. J. Comput. Phys., 60, pp282-304 (1985).
  • J.A.C. Weideman and B.M. Herbst. Split-step methods for the solution of the nonlinear Schroedinger equation. SIAM J. Numer. Anal., 23, pp485-507 (1986).
  • A.R. Mitchell and B.M.~Herbst. Adaptive grids in Petrov-Galerkin computations, in Accuracy Estimates and Adaptivity for Finite Elements, I.~Babushka (ed.). John Wiley (1986).
  • J.A.C. Weideman and B.M. Herbst. Recurrence in semi-discrete approximations of the nonlinear Schroedinger equation. SIAM J. Sci. Stat. Comput., 8, pp988-1004 (1987).
  • B.M. Herbst. Die Einstein-rewolusie, in Varia Studia in honorem W.J. Richards, L. Cilliers en A.H. Snyman (red.). Acta Academia reeks B, U.O.V.S. (1987).
  • A Cloot and B.M. Herbst. Grid resonances, focusing and Benjamin-Feir instabilities in leapfrog time discretizations. J. Comput. Phys., 75, pp31-53 (1988).
  • A Cloot and B.M. Herbst. Analytical instability of the Klein-Gordon equation. J. Comput. Appl. Math., 21, pp17-26 (1988).
  • B.M. Herbst and W.-H. Steeb. Parametrically driven sine-Gordon equation and chaos. Z. Naturforsch, 43a, pp727-733 (1988).
  • B.M. Herbst. The road to chaos in the parametrically driven oscillator, in Finite Dimensional Integrable Nonlinear Dynamical Systems, P.G.L. Leach and W.-H. Steeb (eds.). World Scientific, Singapore (1988).
  • D.M. Sloan and B.M. Herbst. Review of some results on modulational instabilities in nonlinear difference schemes,in Proceedings of the 12th Biennial Conference on Numerical Mathematics, D.F.~Griffiths and G.A.~Watson (eds.). Longman (1988).
  • A Cloot and BM Herbst. A model for the propagation of rounding error in a Klein-Gordon equation. Appl. Numer. Math., 5, pp481-494 (1989).
  • B.M. Herbst and M.J. Ablowitz. Numerically induced chaos in the nonlinear Schroedinger equation. Phys. Rev. Lett., 62, p2065-2068 (1989).
  • B.M. Herbst and M.J. Ablowitz. On numerical chaos in the nonlinear Schroedinger equation, in Integrable Systems and Applications, M. Balabane, P. Lochak and C. Sulem (eds.). Lecture Notes in Physics, Springer-Verlag, Berlin (1989).
  • M.J. Ablowitz and B.M. Herbst. On homoclinic structure and numerically induced chaos in the nonlinear Schroedinger equation. SIAM J. Appl. Math., 50, pp339-351 (1990).
  • A Cloot, BM Herbst and JAC Weideman. A numerical study of the nonlinear Schroedinger equation involving quintic terms. J. Comput. Phys., 86, pp127-146 (1990).
  • M.J. Ablowitz, B.M. Herbst and J.M. Keiser. Nonlinear evolution equations, solitons, chaos and cellular automata, in Nonlinear Physics, Gu Chaohao, Li Yishen and Tu Guizhang (eds.). Research Reports in Physics, Springer-Verlag (1990).
  • M.J. Ablowitz, B.M. Herbst and J.M.~Keiser. Solitons, Numerical Chaos and Cellular Automata, in Integrable and Superintegrable Systems, B. Kupershmidt (ed.). World Scientific Press (1990).
  • M.J. Ablowitz and B.M. Herbst. On homoclinic boundaries in the nonlinear Schroedinger equation, in Hamiltonian Systems, Transformation Groups and Spectral Transform Methods, J. Harnad and J.E. Marsden (eds.), CRM, Montreal (1990).
  • B.M. Herbst, M.J. Ablowitz and E.E. Ryan. Numerical Homoclinic Instabilities and the Complex Modified Korteweg-de Vries Equation. Computer Physics Communications, 65, pp137-142 (1991).
  • B.M. Herbst, J.A.C. Weideman and M.J. Ablowitz. Dynamics of semi-discretizations of the defocusing NLS equation. IMA J. Numer. Anal., 11, pp539-552 (1991).
  • B.M. Herbst and M.J. Ablowitz. Numerical homoclinic instabilities in the sine-Gordon equation. Quaestiones Mathematicae, 15, pp345-363 (1992).
  • Herbst, B. M. Numerical evidence of exponentially small splitting distances in symplectic discretizations of planar Hamiltonian systems. Nonlinear evolution equations and dynamical systems (Baia Verde, 1991), pp207–215, World Sci. Publishing, River Edge, NJ, (1992).
  • B.M. Herbst. Numerical evidence of exponentially small splitting distances in symplectic discretizations of planar Hamiltonian systems, in Nonlinear Evolution Equations and Dynamical Systems, M. Boiti, L. Martina and E. Pempinelli (eds). World Scientific, Singapore (1992).
  • M.P. Robinson, G. Fairweather and B.M. Herbst. On the numerical solution of the cubic Schr”odinger equation in one space variable. J. Comput. Phys., 103, pp277-284 (1993).
  • B.M Herbst and M.J. Ablowitz. Numerical chaos, symplectic integrators and exponentially small splitting distances. J. Comput. Phys., 105, pp122-132 (1993).
  • M.J. Ablowitz, C. Schober and B.M. Herbst. Numerical chaos, roundoff errors and unstable wave processes. Physical Review Letters, 71, pp2683-2686 (1993).
  • M.J. Ablowitz and B.M. Herbst. Solitons and Computation, in Important Developments in Soliton Theory, A.S. Fokas and V.E. Zakharov (eds.). Springer-Verlag, Berlin (1993).
  • Herbst, B. M.; Ablowitz, Mark J. Mel’nikov analysis and numerically induced chaos. Chaos in Australia (Sydney, 1990), 40–56, World Sci. Publishing, River Edge, NJ (1993).
  • B.M. Herbst, F. Varadi and M.J. Ablowitz. Symplectic methods for the nonlinear Schr”odinger equation. Mathematics and Computers in Simulation, 37, pp353-369 (1994).
  • B.M. Herbst, G.J. le Roux and M.J. Ablowitz. Chaos in symplectic discretizations of planar Hamiltonian systems: An overview. In, Proceedings of the International Workshop: From Ordinary Differential Equations to Deterministic Chaos, University of Durban-Westville (1994).
  • M.J. Ablowitz, S. Chakravarty and B.M. Herbst. Integrability, Computation and Applications. Acta Applicandae Mathematicae, 39, pp5-37 (1995).
  • M.J. Ablowitz, B.M. Herbst and C.M. Schober. Numerical simulation of quasi-periodic solutions of the sine-Gordon equation. Physica D, 87,(1995).
  • M.J. Ablowitz, B.M. Herbst and C.M. Schober. On the numerics of integrable discretizations. CRM Proceedings and Lecture Notes, 9, pp1–11 American Mathematical Society (1996).
  • M.J. Ablowitz, B.M. Herbst and C.M. Schober. On the numerical solution of the sine-Gordon equation. I. Integrable discretizations and homoclinic manifolds. J. Comput. Phys., 12, pp299–314 (1996).
  • M.J. Ablowitz, B.M. Herbst and C.M. Schober. Computational chaos in the nonlinear Schroedinger equation without homoclinic crossings. Physica A, 228, pp212–235 (1996).
  • B.M. Herbst, G.J. le Roux and M.J. Ablowitz. Chaos in numerics. In Numerical Analysis. A.R.~Mitchell 75th Birthday Volume, D.F.~Griffiths and G.A.~Watson (eds.). World Scientific, Singapore (1996).
  • J.A.C. Weideman and B.M. Herbst. Finite difference methods for an AKNS problem. Mathematics in Computers and Simulation. 43, pp77–88 (1997).
  • M.J. Ablowitz, B.M. Herbst and C.M. Schober. The nonlinear Schroedinger equation: Asymmetric perturbations, traveling waves and chaotic structures. Mathematics in Computers and Simulation, 43, pp3–12 (1997).
  • M.J. Ablowitz, B.M. Herbst and C.M. Schober. On the numerical solution of the sine-Gordon equation. II. Numerical Studies. J. Comput. Phys., 131, pp354–367 (1997).
  • Herbst, BM, Schober, CM. Chaos in symplectic discretizations of the pendulum and sine-Gordon equations. With comments by A. Mazer and K. L. Teo. Math. Model., 8, Control and chaos (Honolulu, HI, 1995), 39–59, Birkhauser Boston, Boston, MA (1997).
  • B.M. Herbst and C.M. Schober. Chaos in symplectic discretizations of the pendulum and sine-Gordon equations. In Control and Chaos, K. Judd, A. Mees, K.L. Teo and T.L. Vincent (eds.). Birkhauser, Boston (1997).
  • Neil Muller and BM Herbst. The use of eigenpictures for optical character recognition. Proceedings of the 14th International Conference on Pattern Recognition. Volume II. AK Jain, S Venkatesh and BC Lovell eds, pp1124-1126 (1998).
  • Hanno Coetzer and BM Herbst. On an offline signature verification system. Proceedings of the 9th Annual South African Workshop on Pattern Recognition. (DM Weber, BM Herbst and JA du Preez eds), pp39-43 (1998).
  • Neil Muller and BM Herbst. Using interpolation correlation filters to estimate object scale and rotation. Proceedings of the 9th Annual South African Workshop on Pattern Recognition. (DM Weber, BM Herbst and JA du Preez eds), pp107-110 (1998).
  • B.M. Herbst and D.W. Richards. On an automated signature verification system. IEEE Proceedings ISIE‘98, pp600–604, Pretoria (1998).
  • W Black, JAC Weideman and BM Herbst. A note on an integrable discretization of the nonlinear Schroedinger equation. Inverse Problems, 15, pp807-810 (1999).
  • MJ Ablowitz, R Halburd and BM Herbst. On the extension of the Painleve property to difference equations. Nonlinearity, 13, pp889-905 (2000).
  • NL Muller and BM Herbst. On the use of SDF-type filters for distortion invariant image location. Proceedings, 15th International Confrence on pattern Recognition, Volume 3, Asanfeliu, JJ~Villanueva, M~Vanrell, R~Alquezar, T~Huang and J Serra (eds), pp530–533. IEEE Computer Society, Los Alamitos (2000).
  • MJ Ablowitz, BM Herbst and CM Schober. Discretizations, Integrable Systems and Computation. Journal of Physics A, 34, pp10671–10693 (2001).
  • Neil Muller and BM Herbst. On the Use of SDF-type Filters for Distortion Parameter Estimation. IEEE Trans. Pattern Analysis and Machine Intelligence, 24, pp1521-1528(2002).
  • BM Herbst and DW Wagener. Feature based pattern classifier for a patient positioning system. The 7th Intenational Fall Workshop Vision, Modeling and Visualisation 2002, Fraunhofer Institute for Integrated Circuits - Applied Electronics (IIS-A), Erlangen, Germany, AKA, Berlin, pp387-394 (2002).
  • NL Muller and BM Herbst. Extending the linear interpolating condition to advanced synthetic discriminant function variants. International Conference on Pattern Recognition 2002, Quebec City, Canada, IEEE Computer Society, p686 (2002).
  • Johan de Villiers, Karin Goosen and BM Herbst. Dubuc-Deslauriers Subdivision for Finite Sequences and Interpolation Wavelets on an Interval. SIAM J Applied Maths, 35, pp423–452 (2003).
  • BM Herbst, Neil Muller and L Magaia. The singular value decomposition and image processing. SIAM Review, 46, pp518–545 (2004).
  • J Coetzer, BM Herbst and JA du Preez. Off-line signature verification using the discrete Radon transform and a hidden Markov model. EURASIP Journal on Applied Signal Processing, pp559–571 (2004).
  • EM Nel, JA du Preez and BM Herbst. Estimating the pen trajectories of static signatures using Hidden Markov Models. IEEE Trans. Pattern Analysis and Machine Intelligence, 27, pp1733-1746 (2005).
  • EM Nel, JA du Preez and BM Herbst. Estimating the pen trajectories of multi-path static scripts using Hidden Markov Models. Proceedings of the 8th International Conference on Document analysis and Recognition, Seoul, pp41-45 (2005).
  • DF Malan, WH Steyn and BM Herbst. Remote satellite position and pose estimation using moncular vision. Proceedings of the 5th International Symposium of the International Academy of Astronautics. Berlin, pp161-168 (2006).
  • J Coetzer, BM Herbst and JA du Preez. Off-line signature verification: a comparison between human and machine performance. Proceedings of the 10th International Workshop on Frontiers in Handwriting Recognition, La Baule, France, pp. 481-485 (2006).
  • Stefan van der Walt and BM Herbst. Robust automated registration in the spatial domain, In Proceedings of the seventeenth annual symposium of the Pattern Recognition Association of South Africa (PRASA) (2006).
  • McElory Hoffmann, BM Herbst and Karin Hunter. Occlusions and active appearance models. VISAPP, pp441-446 (2007).
  • Stefan van der Walt and BM Herbst. Methods used in increased resolution processing - polygon based interpolation and robust log-polar based registration. VISAPP, pp135-140 (2007).
  • MR Hoffmann, BM Herbst and KM Hunter. On visual tracking using Active Appearance Models. SAIEE Africa Research Journal, 98, pp52–58 (2007).
  • BM Herbst KM Hunter and E Rossouw. Subdivision of curve and surfaces: An overview. SAIEE Africa Research Journal, 98, pp 31–37 (2007).
  • PJ Holtzhausen and BM Herbst. Identity confidence estimation of manoeuvering aircraft. SAIEE Africa Research Journal, 98, pp59–65 (2007).
  • Emli-Mari Nel, Johan A. du Preez and BM Herbst. Verification of dynamic curves extracted from static handwritten scripts. Pattern Recognition, 41, pp 3773-3785 (2008).
  • J de la Porte, BM Herbst, W Hereman and SJ van der Walt. An introduction to diffusion maps. Proceedings Nineteenth Annuals Symposium of Pattern Recognition Society of South Africa, pp125-130 (2008).
  • J Drijer and BM Herbst. Action classification using the average of pose changes. Proceedings Nineteenth Annual Symposium of Pattern Recognition Society of South Africa, pp85-89 (2008).
  • M Hoffmann, KM Hunter and BM Herbst. The hitchhikers guide to the particle filter. Proceedings Nineteenth Annual Symposium of Pattern Recognition Society of South Africa, pp33-38, (2008).
  • M Hoffmann, A Swart, KM Hunter and BM Herbst. Model-based robust and precise tracking embedded in smart cameras-The PFAAM-CAM. 2nd ACM.IEEE International Conference on Distributed Smart Cameras (ICDSC), Stanford University, Stanford, USA, pp1-8, (2008).
  • B.M. van Wyk, N.L. Muller and BM Herbst. Mutual Information based similarity functions for rigid CT-MRI volume registration. Proceedings Twentieth Annual Symposium of Pattern Recognition Society of South Africa, pp105-110 (2009).
  • W Hereman, PJ Adams, HL Eklund, MS Hickman and BM Herbst. Direct methods and symbolic software for conservation laws of nonlinear equations. In Advances in nonlinear waves and symbolic computation, pp1-56, Nova Science Publishers, Inc., New York (2009).
  • EM Nel, JA du Preez and BM Herbst. A pseudo-skeletonization algorithm for static handwritten scripts. International Journal on Document Analysis and Recognition, 12, pp47-62 (2009).
  • DMP Smith, P Meyer and BM Herbst. Image Reconstruction by means of Kalman Filtering in Passive Millimetre-Wave Imaging. Journal of the Serbian Society for Computational Mechanics, 4, Number 1 (2010).
  • Helge Reikeras, BM Herbst, JA du Preez* and H Engelbrecht. Audio-Visual Speech Recognition using SciPy. Proceedings Scipy Conference, Austin Texas (2010).
  • Janto Dreijer, Johan du Preez and BM Herbst. Edge modelling MRFs for cardiac MRI segmentation. Proceedings of the Twenty-First Annual Symposium of the Pattern Recognition Association of South Africa, pp81—86 (2010).
  • Helge Reikeras, BM Herbst, Johan du Preez and Herman Engelbrecht Audio-Visual Automatic Speech Recognition using Dynamic Bayesian Networks. Proceedings of the Twenty-First Annual Symposium of the Pattern Recognition Association of South Africa, pp233—238 (2010).
  • Barry-Michael van Wyk, Neil Muller and BM Herbst. Non-Rigid Image Registration–application to CT-MRI alignment. Proceedings of the Twenty-First Annual Symposium of the Pattern Recognition Association of South Africa, pp289—294 (2010).
  • Yu. V. Pyatkova, D. V. Kamanin, O. V. Falomkina, Yu. R. Pyt’ev, BM Herbst and W. H. Trzaska. Estimating the Reliability of Revealing the Fine Structure in Mass-Kinetic Energy Distributions of Nuclear Reaction Products. To appear Pattern Recognition and Image Analysis (2011).
  • VISAPP2007 Proceedings.

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