Ben Adcock

About me

I am currently an NSERC/PIMS postdoctoral fellow at Simon Fraser University, working with Professor Nilima Nigam. From 2006-2010, I was a PhD student in the Numerical Analysis group at the University of Cambridge under the supervision of Professor Arieh Iserles. My CV can be found here.

In 2011 I received a Leslie Fox Prize for my work on stable reconstructions in Hilbert spaces.

Research Interests

• Numerical analysis, applied and computational harmonic analysis, approximation theory, spectral methods for PDEs, resolution of the Gibbs phenomenon, sampling theory, nonuniform sampling, mathematical signal processing, compressed sensing

Submitted Papers

1. B. Adcock, A. C. Hansen, E. Herrholz and G. Teschke (2011), "Generalized sampling: extensions to frames and inverse and ill-posed problems", DAMTP Tech. Rep. 2011/NA17.
2. B. Adcock, A. C. Hansen, E. Herrholz and G. Teschke (2011), "Generalized sampling, infinite-dimensional compressed sensing, and semi-random sampling for asymptotically incoherent dictionaries", DAMTP Tech. Rep. 2011/NA13.
3. B. Adcock and A. C. Hansen (2011), "Generalized sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients", DAMTP Tech. Rep. 2011/NA12.
4. B. Adcock and A. C. Hansen (2011), "Generalized sampling and infinite-dimensional compressed sensing", DAMTP Tech. Rep. 2011/NA02.
5. B. Adcock and A. C. Hansen (2011), "Sharp bounds, optimality and a geometric interpretation for generalised sampling in Hilbert spaces", DAMTP Tech. Rep. 2011/NA10.
6. B. Adcock and D. Huybrechs (2011), "On the resolution power of Fourier extensions for oscillatory functions", Technical Report TW597, Dept. Computer Science, K.U. Leuven.

Reviewed Journal Papers

1. B. Adcock and A. C. Hansen (2012), "Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon", Appl. Comput. Harm. Anal. (to appear).
2. B. Adcock and A. C. Hansen (2012), "A generalized sampling theorem for stable reconstructions in arbitrary bases", J. Fourier Anal. Appl. (to appear).
3. B. Adcock, A. Iserles and S. P. Nørsett (2012), "From high oscillation to rapid approximation II: Expansions in Birkhoff series", IMA J. Num. Anal. 32(1): 105-140.
4. B. Adcock (2011), "On the convergence of expansions in polyharmonic eigenfunctions", J. Approx. Theory 163(11): 1638-1674.
5. B. Adcock (2011), "Gibbs phenomenon and its removal for a class of orthogonal expansions", BIT 51(1): 7-41.
6. B. Adcock (2011), "Convergence acceleration of modified Fourier series in one or more dimensions", Math. Comp. 80(273): 225-261.
7. B. Adcock (2010), "Multivariate modified Fourier series and application to boundary value problems.", Numer. Math. 115(4): 511-552.
8. B. Adcock (2009), "Univariate modified Fourier methods for second order boundary value problems", BIT 49(2): 249-280.

Proceedings

1. B. Adcock and D. Huybrechs (2011), "Accuracy of the Fourier extension method for oscillatory phenomena", Proceedings of the 10th International Conference on Mathematical and Numerical Aspects of Waves.
2. B. Adcock and A. C. Hansen (2011), "Reduced consistency sampling in Hilbert spaces", Proceedings of the 9th International Conference on Sampling Theory and Applications.
3. B. Adcock and D. Huybrechs (2010), "Multivariate modified Fourier expansions", Proceedings of the 8th International Conference on Spectral and High Order Methods (E. Rønquist et al, ed.).

Essays

1. B. Adcock (2010), "Modified Fourier expansions: theory, construction and applications", PhD thesis.
2. B. Adcock (2008),"Birkhoff-Galerkin methods for linear boundary value problems", Smith-Knight/Rayleigh-Knight Prize.

Recent Seminar/Conference Talks

• "Generalized sampling and infinite-dimensional compressed sensing", UBC SCAIM Seminar, UBC, November 2011.
• "Generalized sampling: a new framework for image and signal reconstruction", Mathematics Colloquium, Arizona State University, October 2011.
• "The computation of stable and accurate Fourier extensions of smooth functions", Computational and Applied Mathematics Seminar, Arizona State University, October 2011.
• "Accuracy of the Fourier extension method for oscillatory phenomena", WAVES 2011, Vancouver, Canada, July 2011.
• "Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon", Leslie Fox Prize Meeting, MIMS, University of Manchester, June 2011.
• "Generalised sampling in Hilbert spaces", EPFL BIG Seminar, EPFL, Lausanne, June 2011.
• Generalised sampling in Hilbert spaces, SampTA 2011, NTU, Singapore, May 2011.
• "A general framework for numerically stable reconstructions in Hilbert spaces", DAMTP Numerical Analysis Seminar, Cambridge, March 2011.
• "A general framework for numerically stable reconstructions in Hilbert spaces", Bath Numerical Analysis Seminar, March 2011.
• "Stable sampling in Hilbert spaces", Canadian Mathematical Society Winter Meeting, Vancouver, December 2010.

Last updated: 18 January 2012