By Associate Professor Robert Womersley

Journal articles

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, vol. 421, pp. 114796 - 114796, 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, vol. 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, vol. 515, pp. 126367 - 126367, 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, vol. 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, vol. 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, vol. 382, pp. 113061 - 113061, 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', , http://arxiv.org/abs/1907.13493v3

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', Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, 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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 27, 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, vol. 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', , http://arxiv.org/abs/1512.07470v2

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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 159, pp. 308 - 318, http://dx.doi.org/10.1016/j.jat.2009.02.014

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, vol. 138, pp. 311 - 328, http://dx.doi.org/10.1007/s10957-008-9355-9

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

Leopardi PC; Womersley RS, 2008, 'Porting a sphere optimization program from LAPACK to ScaLAPACK', The ANZIAM Journal, vol. 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, vol. 10, pp. 239 - 275, http://dx.doi.org/10.1007/s11009-007-9045-3

Chen X; Womersley RS, 2006, 'Existence of solutions to systems of underdetermined equations and spherical designs', SIAM Journal on Numerical Analysis, vol. 44, pp. 2326 - 2341, http://dx.doi.org/10.1137/050626636

Jeyakumar V; Ormerod JT; Womersley RS, 2006, 'Knowledge-based semidefinite linear programming classifiers', Optimization Methods and Software, vol. 21, pp. 693 - 706, http://dx.doi.org/10.1080/10556780500137066

Sloan IH; Womersley RS, 2004, 'Extremal systems of points and numerical integration on the sphere', Advances in Computational Mathematics, vol. 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, vol. 119, pp. 459 - 484, http://dx.doi.org/10.1023/B:JOTA.0000006685.60019.3e

Sun D; Womersley RS; Qi H, 2002, 'A feasible semismooth asymptotically Newton method for mixed complementarity problems', Mathematical Programming, vol. 94, pp. 167 - 187, http://dx.doi.org/10.1007/s10107-002-0305-2

Sloan IH; Womersley RS, 2002, 'Good approximation on the sphere, with application to geodesy and the scattering of sound', Journal of Computational and Applied Mathematics, vol. 149, pp. 227 - 237, http://dx.doi.org/10.1016/S0377-0427(02)00532-0

Womersley RS; Sloan IH, 2001, 'How good can polynomial interpolation on the sphere be?', Advances in Computational Mathematics, vol. 14, pp. 195 - 226, http://dx.doi.org/10.1023/A:1016630227163

Gonsalkorale K; Womersley RS, 2001, 'Multistage quadratic stochastic programming', Journal of Computational and Applied Mathematics, vol. 129, pp. 105 - 138, http://dx.doi.org/10.1016/S0377-0427(00)00545-8

Womersley RS, 2000, 'A continuous minimax problem for calculating minimum norm polynomial interpolation points on the sphere ANZIAM journal', Journal of Australian Mathematical Society B, pp. 1536 - 1557

Sloan IH; Womersley RS, 2000, 'Constructive polynomial approximation on the sphere', Journal of Approximation Theory, vol. 103, pp. 91 - 118, http://dx.doi.org/10.1006/jath.1999.3426

Chen X; Womersley RS, 2000, 'Random test problems and parallel methods for quadratic programs and quadratic stochastic programs', Optimization Methods and Software, vol. 13, pp. 275 - 306, http://dx.doi.org/10.1080/10556780008805789

Sun D; Womersley RS, 1999, 'A new unconstrained differentiable merit function for box constrained variational inequality problems and a damped Gauss-Newton method', SIAM Journal on Optimization, vol. 9, pp. 388 - 413, http://dx.doi.org/10.1137/S1052623496314173

Khoury F; Standish RK; Womersley RS, 1998, 'Parallel triangular system solvers', New South Wales Centre for Parallel Computine, pp. 21 - 22

Chen X; Womersley RS, 1998, 'Stochastic programming', New South Wales Centre for Parallel Computine, pp. 10 - 10

Qi L; Womersley RS, 1996, 'On extreme singular values of matrix valued functions', Journal of Convex Analysis, vol. 3, pp. 153 - 166

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