Numerical analysis preprints, 2001–2010


  1. NA2010/01: Arieh Iserles, "A fast and simple algorithm for the computation of Legendre coefficients"
  2. NA2010/02: B. Adcock, A. Iserles & S.P. Nørsett, "From high oscillation to rapid approximation II: Expansions in Birkhoff series"
  3. NA2010/03: A. Boettcher, H. Brunner, A. Iserles & S.P. Nørsett, "On the Singular Values and Eigenvalues of the Fox–Li and Related Operators"
  4. NA2010/04: M.J.D. Powell, "Beyond symmetric Broyden for updating quadratic models in minimization without derivatives"
  5. NA2010/05: M. Condon, A. Deaño & A. Iserles, "Asymptotic solvers for oscillatory systems of differential equations"
  6. NA2010/06: Ben Adcock, "On the convergence of expansions in polyharmonic eigenfunctions"
  7. NA2010/07: B. Adcock & A.C. Hansen, "A generalized sampling theorem for reconstructions in arbitrary bases"
  8. NA2010/08: A. Boettcher, S.Grudsky, D. Huybrechs & A. Iserles, "First-order trace formulas for the iterates of the Fox–Li operator"
  9. NA2010/09: A. Boettcher, S.Grudsky & A. Iserles, "Spectral theory of large Wiener–Hopf operators with complex-symmetric kernels and rational symbols"
  10. NA2010/10: B. Adcock & A.C. Hansen, "Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon"


  1. NA2009/01: Marianna Khanamirian, "Quadrature methods for highly oscillatory linear and nonlinear systems of ordinary differential equations: Part II"
  2. NA2009/02: Alfredo Deaño & Nico Temme, "Analytical and numerical aspects of a generalization of the complementary error function"
  3. NA2009/03: Hermann Brunner, Arieh Iserles & Syvert Nørsett, "The computation of the spectra of highly oscillatory Fredholm integral operators"
  4. NA2009/04: Daan Huybrechs, Arieh Iserles & Syvert Nørsett, "From high oscillation to rapid approximation V: The equilateral triangle"
  5. NA2009/05: M. Condon, A. Deaño & A. Iserles, "On asyptotic-numerical solvers for differential equations with highly oscillatory forcing terms"
  6. NA2009/06: M.J.D. Powell, "The BOBYQA algorithm for bound constrained optimization without derivatives"
  7. NA2009/07: M. Condon, A. Deaño & A. Iserles, "On second order differential equations with highly oscillatory forcing terms"
  8. NA2009/08: H. Brunner, A. Iserles & S. Nørsett, "On the singular values of the Fox–Li operator": An updated version of this report is NA2010/03.
  9. NA2009/09: M. Condon, A. Deaño & A. Iserles, "On systems of differential equations with extrinsic oscillation"


  1. NA2008/01: Marianna Khanamirian, "Quadrature methods for systems of highly oscillatory ODEs. Part I"
  2. NA2008/02: Anders Hansen, "A theoretical framework for backward error analysis on manifolds"
  3. NA2008/03: M.J.D. Powell, "On nonlinear optimization since 1959"
  4. NA2008/04: Alfredo Deaño & Daan Huybrechs, "Complex Gaussian quadrature of oscillatory integrals"
  5. NA2008/05: Hermann Brunner, Arieh Iserles & Syvert Nørsett, "The spectral problem for a class of highly oscillatory Fredholm differential equations"
  6. NA2008/06: M.J.D. Powell, "On the convergence of a wide range of trust region methods for unconstrained optimization"
  7. NA2008/07: Alfredo Deaño & Nico Temme, "On modified asymptotic series involving confluent hypergeometric functions"
  8. NA2008/08: Ben Adcock, "Sparse grid modified Fourier series and application to boundary value problems"
  9. NA2008/09: Arieh Iserles, "Magnus expansions and beyond"
  10. NA2008/10: Marissa Condon, Alfredo Deaño & Arieh Iserles, "On highly oscillatory problems arising in electronic engineering"
  11. NA2008/11: Ben Adcock, "Convergence acceleration of Fourier-like series in one or more dimensions"
  12. NA2008/12: Marissa Condon, Alfredo Deaño, Arieh Iserles, Kornel Maczynski & Tao Xu, "On numerical methods for highly oscillatory problems in circuit simulation"
  13. NA2008/13: Arieh Iserles & David Levin, "Asymptotic expansion and quadrature of composite highly oscillatory integrals"


  1. NA2007/01: Arieh Iserles & Syvert Nørsett, "From high oscillation to rapid approximation III: Multivariate expansions"
  2. NA2007/02: Sheehan Olver, "On the convergence rate of a modified Fourier series"
  3. NA2007/03: M.J.D. Powell, "A view of algorithms for optimization without derivatives"
  4. NA2007/04: Anders Hansen, "Operator theory and C*-algebras in infinite dimensional numerical linear algebra"
  5. NA2007/05: M.J.D. Powell, "Developments of NEWUOA for unconstrained minimization without derivatives"
  6. NA2007/06: T. Shingel, "Interpolation in special orthogonal groups?
  7. NA2007/07: Daan Huybrechs, Arieh Iserles & Syvert P. Nørsett, "From high oscillation to rapid approximation IV: Accelerating convergence"
  8. NA2007/08: B. Adcock, "Spectral methods & modified Fourier series"


  1. NA2006/01: P.A. Absil & K.A. Gallivan, "Joint diagonalization on the oblique manifold for independent component analysis"
  2. NA2006/02: Anthony M. Bloch, Arieh iserles, Jerrold E. Marsden & Tudor S. Ratiu, "A class of integrable geodesic flows on the symplectic group & the symmetric matrices"
  3. NA2006/03: R.K. Beatson, M.J.D. Powell & A.M. Tan, "Fast evaluation of polyharmonic splines in three dimensions"
  4. NA2006/04: Arieh Iserles, Reinout Quispel & Priscilla Tse, "B-series methods cannot be volume preserving"
  5. NA2006/05: Arieh Iserles & Syvert Nørsett, "From high oscillation to rapid approximation I: Modified Fourier expansions"
  6. NA2006/06: Sheehan Olver, "Numerical approximation of vector-valued highly oscillatory integrals"
  7. NA2006/07: Arieh Iserles & Syvert Nørsett, "From high oscillation to rapid approximation II: Expansions in polyharmonic eigenfunctions": An updated version of this report is NA2010/02.
  8. NA2006/08: Sergio Blanes, Fernando Casas & Ander Murua, "On the linear stability of splitting methods"
  9. NA2006/09: Sheehan Olver, "Moment-free numerical approximation of highly oscillatory integrals with stationary points"


  1. NA2005/01: A.M. Bloch & A. Iserles, "On an isospectral Lie–Poisson system & its Lie algebra"
  2. NA2005/02: Arieh Iserles & S.P. Nørsett, "Quadrature methods for multivariate highly oscillatory integrals using derivatives"
  3. NA2005/03: Simon Foucart, "Interlacing property for B-splines"
  4. NA2005/04: Sheehan Olver, "Moment-free numerical integration of highly oscillatory functions"
  5. NA2005/05: Fernando Casas & Arieh Iserles, "Explicit Magnus expansions for nonlinear equations"
  6. NA2005/06: Arieh Iserles, Syvert P. Nørsett & Sheehan Olver, "Highly oscillatory quadrature: The story so far"
  7. NA2005/07: Sheehan Olver, "On the quadrature of multivariate highly oscillatory integrals over non-polytope domains"
  8. NA2005/08: Arieh Iserles & Syvert P. Nørsett, "On the computation of highly oscillatory multivariate integrals with critical points"
  9. NA2005/09: Simon Foucart, "On the value of the max-norm of the orthogonal projector onto splines with multiple knots"


  1. NA2004/01: M.J.D. Powell, "On updating the inverse of a KKT matrix"
  2. NA2004/02: Arieh Iserles, "On the method of Neumann series for highly oscillatory equations"
  3. NA2004/03: Arieh Iserles & S.P. Nørsett, "Efficient quadrature of highly oscillatory integrals using derivatives"
  4. NA2004/04: Tony Bloch & Arieh iserles, "Commutators of skew-symmetric matrices"
  5. NA2004/05: Arieh Iserles & S.P. Nørsett, "On quadrature methods for highly oscillatory integrals and their implementation"
  6. NA2004/06: B.J.C. Baxter & R. Brummelhuis, "Exponential Brownian motion & divided differences"
  7. NA2004/07: A.S. Fokas, A. Iserles & V. Marinakis, "Reconstruction algorithms for positron emission tomography and single photon emission computed tomography and their numerical implementation"
  8. NA2004/08: M.J.D. Powell, "The NEWUOA software for unconstrained optimization without derivatives"


  1. NA2003/01: Tony Bloch & Arieh iserles, "Optimality of double bracket flows and generalized double bracket flows"
  2. NA2003/02: Arieh Iserles & Antonella Zanna, "On the spectra of certain matrices generated by involutory automorphisms"
  3. NA2003/03: M.J.D. Powell, "On the use of quadratic models in unconstrained minimization without derivatives"
  4. NA2003/04: Tony Bloch & Arieh iserles, "On the optimality of double-bracket flows"
  5. NA2003/05: Arieh Iserles, "On the numerical quadrature of highly-oscillating integrals I: Fourier transforms"
  6. NA2003/06: Arieh Iserles, "On the numerical analysis of rapid oscillation"
  7. NA2003/07: Anthony M. Bloch & Arieh iserles, "Aspects of generalized double-bracket flows"
  8. NA2003/08: Brad Baxter, "Positive definite functions on Hilbert space"
  9. NA2003/09: Arieh Iserles, "On the numerical quadrature of highly-oscillating integrals II: Irregular oscillators"
  10. NA2003/10: Simon Foucart "On the best conditioned bases of quadratic polynomials"


  1. NA2002/01: Arieh Iserles, "Expansions that grow on trees"
  2. NA2002/02: M.J.D. Powell, "On trust region methods for unconstrained minimization without derivatives"
  3. NA2002/03: Nicoleta Bila, "Symmetry reductions, variational symmetries & conservation laws for shallow water & semi-geostrophic PDE systems"
  4. NA2002/04: Kirill Kopotun & Alexei Shadrin, "On k-monotone approximation by free knot splines"
  5. NA2002/05: A.C. Faul, G. Goodsell & M.J.D. Powell, "A Krylov subspace algorithm for multiquadric interpolation in many dimensions"
  6. NA2002/06: N. Bila & J. Niesen, "On a new procedure for finding nonclassical symmetries"
  7. NA2002/07: B.J.C. Baxter & A. Iserles, "On the foundations of computational mathematics"
  8. NA2002/08: M.J.D. Powell, "Least Frobenius norm updating of quadratic models that satisfy interpolation conditions"
  9. NA2002/09: Arieh Iserles & Antonella Zanna, "Efficient computation of the matrix exponential by generalized polar decompositions"


  1. NA2001/01: G. Zhao & F. Meng, "On smoothness of the Moreau–Yosida regularization of a Lagrangian-dual function"
  2. NA2001/02: X. Liu, K.-C. Toh & G. Zhao, "On implementation of a Lagrangian dual method for solving multi-stage stochastic programming problems"
  3. NA2001/03: R.A. Hauser & O. Güler, "Self-scaled barrier functions on symmetric cones and their classification"
  4. NA2001/04: R.A. Hauser & Y. Lim, "Self-scaled barriers for irreducible symmetric cones"
  5. NA2001/05: Sergio Blanes, "Symplectic integrators for polynomial Hamiltonians with applications to accelerator physics"
  6. NA2001/06: Arieh Iserles, "Think globally, act locally: solving highly-oscillatory ordinary differential equations"
  7. NA2001/07: Jitse Niesen, "A priori estimates for the global error committed by Runge–Kutta methods for a nonlinear oscillator"
  8. NA2001/08: Arieh Iserles, "On the discretization of double-bracket flows"
  9. NA2001/09: M.D. Buhmann, A. Iserles & S.P. Nørsett, "Applications of radial basis functions: Sobolev-orthogonal functions, radial basis functions and spectral methods"
  10. NA2001/10: Arieh Iserles, "Brief introduction to Lie-group methods"
  11. NA2001/11: M.J.D. Powell, "Radial basis function methods for interpolation to functions of many variables"