By Associate Professor Robert Womersley

Books

, 1997, Computational nonsmooth optimization, Qi L; Ruszczynski A; Womersley RS, (eds.), Mathematical Programming Society, North Holland

Du D-Z; Qi L; Womersley RS, 1995, Recent Advances in Nonsmooth Optimization, WORLD SCIENTIFIC, http://dx.doi.org/10.1142/2752

Book Chapters

Brauchart JS; Dragnev PD; Saff EB; Womersley RS, 2018, 'Logarithmic and riesz equilibrium for multiple sources on the sphere: The exceptional case', in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, pp. 179 - 203, http://dx.doi.org/10.1007/978-3-319-72456-0_10

Hesse K; Sloan IH; Womersley RS, 2015, 'Numerical integration on the sphere', in Handbook of Geomathematics: Second Edition, Springer Nature, pp. 2671 - 2710, http://dx.doi.org/10.1007/978-3-642-54551-1_40

Hesse K; Sloan IH; Womersley RS, 2015, 'Numerical Integration on the Sphere', in Handbook of Geomathematics, Springer Berlin Heidelberg, pp. 1 - 35, http://dx.doi.org/10.1007/978-3-642-27793-1_40-3

Hesse K; Sloan IH; Womersley RS, 2013, 'Numerical Integration on the Sphere', in Handbook of Geomathematics, Springer Berlin Heidelberg, pp. 1 - 35, http://dx.doi.org/10.1007/978-3-642-27793-1_40-2

Hesse K; Sloan IH; Womersley RS, 2010, 'Numerical Integration on the Sphere', in Freeden W; Nashed MZ; Sonar T (ed.), Handbook of Geomathematics, Springer, Berlin, pp. 1187 - 1220

Hesse K; Sloan IH; Womersley RS, 2010, 'Numerical Integration on the Sphere', in Handbook of Geomathematics, Springer Berlin Heidelberg, pp. 1185 - 1219, http://dx.doi.org/10.1007/978-3-642-01546-5_40

Journal articles

Brauchart JS; Grabner PJ; Sloan IH; Womersley RS, 2024, 'Needlets liberated', Applied and Computational Harmonic Analysis, 73, http://dx.doi.org/10.1016/j.acha.2024.101693

Hamann J; Le Gia QT; Sloan IH; Womersley RS, 2024, 'Removing the mask—reconstructing a real-valued field on the sphere from a masked field by spherical fourier analysis', SIAM Journal on Imaging Sciences, 17, pp. 1820 - 1843, http://dx.doi.org/10.1137/23M1603157

Wang YG; Womersley RS; Wu HT; Yu WH, 2023, 'Numerical computation of triangular complex spherical designs with small mesh ratio', Journal of Computational and Applied Mathematics, 421, http://dx.doi.org/10.1016/j.cam.2022.114796

Chafaï D; Saff EB; Womersley RS, 2023, 'Threshold condensation to singular support for a Riesz equilibrium problem', Analysis and Mathematical Physics, 13, http://dx.doi.org/10.1007/s13324-023-00779-w

Chafaï D; Saff EB; Womersley RS, 2022, 'On the solution of a Riesz equilibrium problem and integral identities for special functions', Journal of Mathematical Analysis and Applications, 515, http://dx.doi.org/10.1016/j.jmaa.2022.126367

Sourisseau M; Wang YG; Womersley RS; Wu HT; Yu WH, 2021, 'Improve concentration of frequency and time (ConceFT) by novel complex spherical designs', Applied and Computational Harmonic Analysis, 54, pp. 137 - 144, http://dx.doi.org/10.1016/j.acha.2021.02.003

Hamann J; Le Gia QT; Sloan IH; Wang YG; Womersley RS, 2021, 'A new probe of Gaussianity and isotropy with application to cosmic microwave background maps', International Journal of Modern Physics C, 32, http://dx.doi.org/10.1142/S0129183121500844

Hesse K; Sloan IH; Womersley RS, 2021, 'Local RBF-based penalized least-squares approximation on the sphere with noisy scattered data', Journal of Computational and Applied Mathematics, 382, http://dx.doi.org/10.1016/j.cam.2020.113061

Sourisseau M; Wang YG; Womersley RS; Wu H-T; Yu W-H, 2020, 'Improve Concentration of Frequency and Time (Conceft) by Novel Complex Spherical Designs', , http://dx.doi.org/10.1101/2020.11.23.394007

Wang YG; Womersley RS; Wu H-T; Yu W-H, 2019, 'Numerical computation of triangular complex spherical designs with small mesh ratio',

Gia QTL; Sloan IH; Womersley RS; Wang YG, 2019, 'Isotropic sparse regularization for spherical harmonic representations of random fields on the sphere', Applied and Computational Harmonic Analysis, http://dx.doi.org/10.1016/j.acha.2019.01.005

Womersley RS, 2018, 'Efficient spherical designs with good geometric properties', , pp. 1243 - 1285, http://dx.doi.org/10.1007/978-3-319-72456-0_57

Brauchart JS; Reznikov AB; Saff EB; Sloan IH; Wang YG; Womersley RS, 2018, 'Random Point Sets on the Sphere—Hole Radii, Covering, and Separation', Experimental Mathematics, 27, pp. 62 - 81, http://dx.doi.org/10.1080/10586458.2016.1226209

Brauchart JS; Reznikov AB; Saff EB; Sloan IH; Wang YG; Womersley RS, 2018, 'Random Point Sets on the Sphere—Hole Radii, Covering, and Separation', Experimental Mathematics, 27, pp. 62 - 81, http://dx.doi.org/10.1080/10586458.2016.1226209

Brauchart JS; Reznikov AB; Saff EB; Sloan IH; Wang YG; Womersley RS, 2018, 'Random Point Sets on the Sphere—Hole Radii, Covering, and Separation', Experimental Mathematics, 27, pp. 62 - 81, http://dx.doi.org/10.1080/10586458.2016.1226209

Brauchart JS; Reznikov AB; Saff EB; Sloan IH; Wang YG; Womersley RS, 2018, 'Random Point Sets on the Sphere-Hole Radii, Covering, and Separation', EXPERIMENTAL MATHEMATICS, 27, pp. 62 - 81, http://dx.doi.org/10.1080/10586458.2016.1226209

Chen X; Womersley RS, 2018, 'Spherical designs and nonconvex minimization for recovery of sparse signals on the sphere', SIAM Journal on Imaging Sciences, 11, pp. 1390 - 1415, http://dx.doi.org/10.1137/17M1147378

Hesse K; Sloan IH; Womersley RS, 2017, 'Radial basis function approximation of noisy scattered data on the sphere', Numerische Mathematik, 137, pp. 579 - 605, http://dx.doi.org/10.1007/s00211-017-0886-6

Wang YG; Le Gia QT; Sloan IH; Womersley RS, 2017, 'Fully discrete needlet approximation on the sphere', Applied and Computational Harmonic Analysis, 43, pp. 292 - 316, http://dx.doi.org/10.1016/j.acha.2016.01.003

Le Gia QT; Sloan IH; Wang YG; Womersley RS, 2017, 'Needlet approximation for isotropic random fields on the sphere', Journal of Approximation Theory, 216, pp. 86 - 116, http://dx.doi.org/10.1016/j.jat.2017.01.001

Brauchart JS; Reznikov AB; Saff EB; Sloan IH; Wang YG; Womersley RS, 2016, 'Random Point Sets on the Sphere—Hole Radii, Covering, and Separation', Experimental Mathematics, pp. 1 - 20, http://dx.doi.org/10.1080/10586458.2016.1226209

Wang YG; Sloan IH; Womersley RS, 2016, 'Riemann Localisation on the Sphere', Journal of Fourier Analysis and Applications, 24, pp. 1 - 43, http://dx.doi.org/10.1007/s00041-016-9496-4

Brauchart JS; Reznikov AB; Saff EB; Sloan IH; Wang YG; Womersley RS, 2015, 'Random Point Sets on the Sphere --- Hole Radii, Covering, and Separation',

Brauchart JS; Dick J; Saff EB; Sloan IH; Wang YG; Womersley RS, 2015, 'Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces', Journal of Mathematical Analysis and Applications, 431, pp. 782 - 811, http://dx.doi.org/10.1016/j.jmaa.2015.05.079

Brauchart JS; Saff EB; Sloan IH; Womersley RS, 2014, 'QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere', Mathematics of Computation, 83, pp. 2821 - 2851, http://dx.doi.org/10.1090/S0025-5718-2014-02839-1

An C; Chen X; Sloan IH; Womersley RS, 2014, 'Erratum: Regularized least squares approximations on the sphere using spherical designs (SIAM Journal on Numerical Analysis (2012) 50 (1513-1534))', SIAM Journal on Numerical Analysis, 52, pp. 2205 - 2206, http://dx.doi.org/10.1137/140962504

Chernih A; Sloan IH; Womersley RS, 2014, 'Wendland functions with increasing smoothness converge to a Gaussian', Advances in Computational Mathematics, 40, pp. 185 - 200, http://dx.doi.org/10.1007/s10444-013-9304-5

Sloan IH; Womersley RS, 2012, 'Filtered hyperinterpolation: a constructive polynomial approximation on the sphere', International Journal on Geomathematics, 3, pp. 95 - 117, http://dx.doi.org/10.1007/s13137-011-0029-7

Hesse K; Womersley RS, 2012, 'Numerical integration with polynomial exactness over a spherical cap', Advances in Computational Mathematics, 36, pp. 451 - 483, http://dx.doi.org/10.1007/s10444-011-9187-2

An C; Chen X; Sloan IH; Womersley RS, 2012, 'Regularized least squares approximations on the sphere using spherical designs', SIAM Journal on Numerical Analysis, 50, pp. 1513 - 1534, http://dx.doi.org/10.1137/110838601

Chen X; Womersley RS; Ye JJ, 2011, 'Minimizing the condition number of a gram matrix', SIAM Journal on Optimization, 21, pp. 127 - 148, http://dx.doi.org/10.1137/100786022

An C; Chen X; Sloan IH; Womersley RS, 2010, 'Well conditioned spherical designs for integration and interpolation on the two-sphere', SIAM Journal on Numerical Analysis, 48, pp. 2135 - 2157, http://dx.doi.org/10.1137/100795140

Sloan IH; Womersley RS, 2009, 'A variational characterisation of spherical designs', Journal of Approximation Theory, 159, pp. 308 - 318

Polak E; Womersley RS; Yin H, 2008, 'An algorithm based on active sets and smoothing for discretized semi-infinile minimax problems', Journal of Optimization Theory and Applications

Evans JR; Womersley RS; Wong D; Woodbury G, 2008, 'Operational Risk in Banks', JASSA - Journal of the Securities Institute of Australia, 2, pp. 9 - 16

Leopardi PC; Womersley RS, 2008, 'Porting a sphere optimization program from LAPACK to ScaLAPACK', The ANZIAM Journal, 50, pp. C204 - C219

Kuo FY; Dunsmuir WT; Sloan IH; Wand MP; Womersley RS, 2008, 'Quasi-Monte Carlo for highly structured generalised response models', Methodology and Computing in Applied Probability, 10, pp. 239 - 275

Chen X; Womersley RS, 2006, 'Existence of solutions to systems of underdetermined equations and spherical designs', SIAM Journal on Numerical Analysis, 44, pp. 2326 - 2341

Jeyakumar V; Ormerod JT; Womersley RS, 2006, 'Knowledge-based semidefinite linear programming classifiers', Optimization Methods and Software, 21, pp. 693 - 706

Sloan IH; Womersley RS, 2004, 'Extremal systems of points and numerical integration on the sphere', Advances in Computational Mathematics, 21, pp. 107 - 125

Polak E; Royset JO; Womersley RS, 2003, 'Algorithms with adaptive smoothing for finite minimax problems', Journal of Optimization Theory and Applications, 119, pp. 459 - 484

Sun D; Womersley RS; Qi H, 2002, 'A feasible semismooth asymptotically Newton method for mixed complementarity problems', Mathematical Programming, 94, pp. 167 - 187

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