Numerical analysis preprints, 1994–2000


  1. NA2000/01: A. Bejancu, "On the accuracy of surface spline approximation and interpolation to bump functions"
  2. NA2000/02: R. Hauser, "Self-scaled barriers for semidefinite programming"
  3. NA2000/03: A. Iserles, H.Z. Munthe-Kaas, S.P. Nørsett & A. Zanna, "Lie-group methods"
  4. NA2000/04: H.-M. Gutmann, "On the semi-norm of radial basis function interpolants"
  5. NA2000/05: S. Blanes, "High order numerical integrators for differential equations using composition and processing of low order methods"
  6. NA2000/06: A. Iserles, "Numerical analysis in Lie groups"
  7. NA2000/07: S. Blanes, F. Casas & J. Ros, "High order optimized geometric integrators for linear differential equations"
  8. NA2000/08: A. Bejancu, "A new approach to semi-cardinal spline interpolation"
  9. NA2000/09: A. Bejancu, "Polyharmonic spline interpolation on a semi-space lattice"
  10. NA2000/10: M.J.D. Powell, "On the Lagrange functions of quadratic models that are defined by interpolation"
  11. NA2000/11: A. Iserles, "On the global error of discretization methods for highly-oscillatory ordinary differential equations"
  12. NA2000/12: A. Iserles, "A Magnus expansion for the equation Y'=AY-YB"
  13. NA2000/13: S. Blanes & P.C. Moan, "Practical symplectic partitioned Runge–Kutta & Runge–Kutta–Nyström methods"
  14. NA2000/14: M.J.D. Powell, "UOBYQA: unconstrained optimization by quadratic approximation"


  1. NA1999/01: Arieh Iserles, "How large is the exponential of a banded matrix?"
  2. NA1999/02: Antonella Zanna, Kenth Engø & Hans Z. Munthe-Kaas, "Adjoint & selfadjoint Lie-group methods"
  3. NA1999/03: Elena Celledoni & Arieh Iserkes, "Methods for the approximation of the matrix exponential in a Lie-algebraic setting"
  4. NA1999/04: Arieh Iserles, "On Cayley-transform methods for the discretization of Lie-group equations"
  5. NA1999/05: Malcolm Sabin, "Explorations in 3D integer based linear geometry"
  6. NA1999/06: Arieh Iserles & Antonella Zanna, "On the dimension of certain graded Lie algebras arising in geometric integration of differential equations"
  7. NA1999/07: M.J.D. Powell, "On the convergence of the DFP algorithm for unconstrained optimization when there are only two variables"
  8. NA1999/08: S. Blanes, F. Casas & J. Ros, "Improved high order integrators based on Magnus expansion"
  9. NA1999/09: S. Blanes, F. Casas & J. Ros, "Extrapolation of symplectic integrators"
  10. NA1999/10: S. Blanes, L. Jodar & E. Ponsoda, "Approximate solutions with a priori error bounds for continuous-coefficient matrix Riccati equations"
  11. NA1999/11: A.C. Faul & M.J.D. Powell, "Krylov subspace methods for radial basis function interpolation"
  12. NA1999/12: Arieh Iserles & Antonella Zanna, "Preserving algebraic invariants with Runge–Kutta methods"
  13. NA1999/13: R. Hauser, "Self-scaled barrier functions: Decomposition and classification"
  14. NA1999/14: R. Hauser, "Square-root fields & the 'V-space' approach to primal-dual interior-point methods for self-scaled conic programming"
  15. NA1999/15: R. Hauser, "Target directions for primal-dual interior-point methods for self-scaled conic programming"
  16. NA1999/16: R. Hauser, "Primal-dual symmetric scale-invariant square-root fields for isotropic self-scaled barrier functionals"
  17. NA1999/17: R. Hauser, "Nesterov–Todd directions are Newton directions"
  18. NA1999/18: K. Engø & S. Faltinsen, "Numerical integration of Lie–Poisson systems while preserving coadjoint orbits and energy"
  19. NA1999/19: S. Blanes & P.C. Moan, "Splitting methods for the time-dependent Schrödinger equation"
  20. NA1999/20: E. Celledoni, A. Iserles, S.P. Nørsett & B. Orel, "Complexity theory for Lie-group solvers"
  21. NA1999/21: S. Blanes & P.C. Moan, "Splitting Methods for non-autonomous differential equations"
  22. NA1999/22: H.-M. Gutmann, "A radial basis function method for global optimization"


  1. NA1998/01: Yungkang Liu, "Projected Runge–Kutta methods for differential equations on matrix Lie groups"
  2. NA1998/02: Arieh Iserles, Arne Marthinsen & Syvert Nørsett, "On the implementation of the method of Magnus series for linear differential equations"
  3. NA1998/03: Elena Celledoni & Arieh Iserles, "Approximating the exponential from a Lie algebra to a Lie group"
  4. NA1998/04: M.J.D. Powell, "Direct search algorithms for optimization calculations"
  5. NA1998/05: M.J.D. Powell, "Recent research in Cambridge on radial basis functions"
  6. NA1998/06: A. Iserles, S.P. Nørsett & A.F. Rasmussen, "Time-symmetry and high-order Magnus methods"
  7. NA1998/07: A. Iserles, "Lie groups & the computation of invariants"
  8. NA1998/08: A.C. Faul & M.J.D. Powell, "Proof of convergence of an iterative technique for thin plate spline interpolation in two dimensions"
  9. NA1998/09: V. Shapiro & M. Sabin, "Modifications in cellular modelling"
  10. NA1998/10: C.J. Budd & A. Iserles "Geometric integration: Numerical solution of differential equations on manifolds"
  11. NA1998/11: P.C. Moan, "Efficient approximation of Sturm–Liouville problems using Lie-group methods"
  12. NA1998/12: S. Faltinsen, "Backward error analysis for Lie-group methods"
  13. NA1998/13: Yunkang Liu, "Calculation of discrete relaxation modulus and creep compliance in rheology"
  14. NA1998/14: Antonella Zanna, "The Fer expansion and time-symmetry: a Strang-type approach"


  1. NA1997/01: George Goodsell, "On finding p-th nearest neighbours of scattered points in two dimensions for small p"
  2. NA1997/02: Antonella Zanna, "Lie-group methods for isospectral flows"
  3. NA1997/03: Arieh Iserles & Syvert P. Nørsett, "On the solution of linear differential equations in Lie groups"
  4. NA1997/04: Yungkang Liu, "Numerical solution of implicit neutral functional differential equations"
  5. NA1997/05: Ayla Kol, Brian Laird & Benedict Leimkuhler, "A symplectic method for rigid-body molecular simulation"
  6. NA1997/06: Yungkang Liu, "Existence, uniqueness & continuous dependence for neutral equations with state-dependent delays"
  7. NA1997/07: Aurelian Bejancu, "The uniform convergence of multivariate natural splines"
  8. NA1997/08: Benedict Leimkuhler, "Reversible adaptive regularization I: perturbed Kepler motion and classical atomic trajectories"
  9. NA1997/09: Arieh Iserles & Syvert P. Nørsett, "Linear ODEs in Lie groups"
  10. NA1997/10: Arieh Iserles, "Insight, not just numbers"
  11. NA1997/11: Andreas Dullweber, Benedict Leimkuhler & Robert McLachlan, "Split-Hamiltonian methods for rigid body molecular dynamics"
  12. NA1997/12: M.J.D. Powell, "The use of band matrices for second derivative approximations in trust region algorithms"
  13. NA1997/13: Arieh Iserles , "Multistep methods on manifolds"
  14. NA1997/14: Hans Munthe-Kaas, "High-order Runge–Kutta methods on manifolds"
  15. NA1997/15: Yungkang Liu, "Numerical solution of the heat equation with nonlocal boundary conditions"
  16. NA1997/16: Mari Paz Calvo, Arieh Iserles & Antonella Zanna, "Semi-explicit methods for isospectral flows"
  17. NA1997/17: Antonella Zanna, "Collocation & relaxed collocation for the Fer &and the Magnus expansions" (Revised version, with added numerical experiments)
  18. NA1997/18: M.J.D. Powell, "Trust region calculations revisited"
  19. NA1997/19: Aurelian Bejancu, "Local accuracy for radial basis function interpolation on finite uniform grids"
  20. NA1997/20: Yungkang Liu, "Runge–Kutta–collocation methods for systems of functional-differential and functional equations"
  21. NA1997/21: M.J.D. Powell, "An optimal way of moving a sequence of points onto a curve in two dimensions"
  22. NA1997/22: Arieh Iserles, Robert McLachlan & Antonella Zanna, "Approximately preserving symmetries in numerical integration"


  1. NA1996/01: Gregory Derfel & Arieh Iserles , "The pantograph equation in the complex plane"
  2. NA1996/02: George Goodsell, "A multigrid-type method for thin plate spline interpolation on a circle"
  3. NA1996/05: B.J.C. Baxter & A. Iserles, "On approximation by exponentials"
  4. NA1996/06: A. Iserles, G. Ramaswami & M. Sofroniou, "Runge–Kutta methods for quadratic ordinary differential equations"
  5. NA1996/07: Arieh Iserles & Antonella Zanna, "A scalpel, not a sledgehammer: Qualitative approach to numerical mathematics"
  6. NA1996/08: Mari Paz Calvo, Arieh Iserles & Antonella Zanna, "Runge–Kutta methods for orthogonal and isospectral flows"
  7. NA1996/09: Arieh Iserles, "Beyond the classical theory of computational ordinary differential equations"
  8. NA1996/10: Arieh Iserles, "Exact and discretized stability of the pantograph equation"
  9. NA1996/12: Antonella Zanna, "The method of iterated commutators for ordinary differential equations on Lie groups"
  10. NA1996/13: Arieh Iserles, "Numerical methods on (and off) manifolds"
  11. NA1996/14: Antonella Zanna & Hans Munthe-Kaas, "Iterated commutators, Lie's reduction method and ordinary differential equations on matrix Lie groups"
  12. NA1996/15: Hans Munthe-Kaas & Antonella Zanna, "Numerical integration of differential equations on homogeneous manifolds"
  13. NA1996/16: Alan Feldstein & Yungkang Liu, "On neutral functional-differential equations with variable time delays"
  14. NA1996/17: Malcolm Sabin, "Pseudo-quadratic rational speed splines"
  15. NA1996/18: Mari Paz Calvo, Arieh Iserles & Antonella Zanna, "Conservative methods for the Toda lattice equations"
  16. NA1996/19: Yungkang Liu, "On a functional Riccati equation"


  1. NA1995/03: Mari Paz Calvo, Arieh Iserles & Antonella Zanna, "Numerical solution of isospectral flows"
  2. NA1995/04: Sigitas Keras, "Waveform relaxation method with Toeplitz operator splitting"
  3. NA1995/05: Arieh Iserles & Antonella Zanna, "Qualitative numerical analysis of ordinary differential equations"
  4. NA1995/06: Arieh Iserles & Yunkang Liu, "Integro-differential equations and generalized hypergeometric functions"
  5. NA1995/07: Sigitas Keras, "Combining domain decomposition with waveform relaxation"
  6. NA1995/09: Mari Paz Calvo, Arieh Iserles & Antonella Zanna, "Runge–Kutta methods on manifolds"


  1. NA1994/02: Arieh Iserles & Syvert P. Nørsett, "Biorthogonal polynomials and zero-mapping transformations"
  2. NA1994/04: Arieh Iserles & Syvert P. Nørsett, "Explicit representations of biorthogonal polynomials"
  3. NA1994/06: Sigitas Keras, "Spurious chaotic solutions of differential equations"
  4. NA1994/08: Arieh Iserles, "Biorthogonal polynomials: Recent developments"