Associate Professor Robert Womersley

Honorary Associate Professor

PhD, MSc University of Dundee, BSc (Hons) Adelaide University

Science

School of Mathematics & Statistics

I was a staff member of the School of Mathematics and Statistics from 1985 to 2015, and an honorary since then.

I have held visiting/short term positions at Vanderbilt University, ICERM, Hong Kong Polytechnic University, Argonne National Laboratory, Courant Institute, Australian National University and University of Kentucky.

E-mail

R.Womersley@unsw.edu.au

Location

School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre Room 1037

Books | 1997

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

Books | 1995

Du D-Z; Qi L; Womersley RS, 1995, Recent Advances in Nonsmooth Optimization, WORLD SCIENTIFIC, http://dx.doi.org/10.1142/2752
Book Chapters | 2018

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

Book Chapters | 2015

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

Book Chapters | 2015

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

Book Chapters | 2013

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

Book Chapters | 2010

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

Book Chapters | 2010

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
Journal articles | 2024

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

Journal articles | 2024

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

Journal articles | 2023

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

Journal articles | 2023

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, pp. 114796 - 114796, http://dx.doi.org/10.1016/j.cam.2022.114796

Journal articles | 2022

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

Journal articles | 2021

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

Journal articles | 2021

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

Journal articles | 2021

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

Journal articles | 2020

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

Journal articles | 2019

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

Journal articles | 2019

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

Journal articles | 2018

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

Journal articles | 2018

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

Journal articles | 2018

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

Journal articles | 2018

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

Journal articles | 2018

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

Journal articles | 2018

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

Journal articles | 2017

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

Journal articles | 2017

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

Journal articles | 2017

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

Journal articles | 2016

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, 27, pp. 1 - 20, http://dx.doi.org/10.1080/10586458.2016.1226209

Journal articles | 2016

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

Journal articles | 2015

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

Journal articles | 2015

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

Journal articles | 2014

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

Journal articles | 2014

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

Journal articles | 2014

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

Journal articles | 2012

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

Journal articles | 2012

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

Journal articles | 2012

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

Journal articles | 2011

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

Journal articles | 2010

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

Journal articles | 2009

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

Journal articles | 2008

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

Journal articles | 2008

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

Journal articles | 2008

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

Journal articles | 2008

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

Journal articles | 2006

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

Journal articles | 2006

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

Journal articles | 2004

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

Journal articles | 2003

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

Journal articles | 2002

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, 149, pp. 227 - 237

Journal articles | 2002

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

Journal articles | 2001

Gonsalkorale K; Womersley RS, 2001, 'Multistage quadratic stochastic programming', Journal of Computational and Applied Mathematics, 129, pp. 105 - 138

Journal articles | 2001

Womersley RS; Sloan IH, 2001, 'How good can polynomial interpolation on the sphere be?', Advances in Computational Mathematics, 14, pp. 195 - 226

Journal articles | 2000

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

Journal articles | 2000

Sloan IH; Womersley RS, 2000, 'Constructive polynomial approximation on the sphere', Journal of Approximation Theory, 103, pp. 91 - 118

Journal articles | 2000

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

Journal articles | 1999

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, 9, pp. 388 - 413, http://dx.doi.org/10.1137/S1052623496314173

Journal articles | 1998

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

Journal articles | 1998

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

Journal articles | 1996

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

Journal articles | 1996

Tin Loi FS; Qi L; Wei Z; Womersley RS, 1996, 'Stochastic ultimate load analysis: models and solution methods', Numerical Functional Analysis and Optimization, 17, pp. 1029 - 1043, http://dx.doi.org/10.1080/01630569608816740

Journal articles | 1995

Chen X; Qi L; Womersley RS, 1995, 'Newton's method for quadratic stochastic programs with recourse', Journal of Computational and Applied Mathematics, 60, pp. 29 - 46, http://dx.doi.org/10.1016/0377-0427(94)00082-C

Journal articles | 1995

Overton ML; Womersley RS, 1995, 'Second derivatives for optimizing eigenvalues of symmetric matrices', SIAM Journal on Matrix Analysis and Applications, 16, pp. 697 - 718

Journal articles | 1995

Qi L; Womersley RS, 1995, 'An SQP algorithm for extended linear-quadratic problems in stochastic programming', Annals of Operations Research, pp. 251 - 285

Journal articles | 1993

Overton ML; Womersley RS, 1993, 'Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices', Mathematical Programming, 62, pp. 321 - 357, http://dx.doi.org/10.1007/BF01585173

Journal articles | 1992

Overton ML; Womersley RS, 1992, 'On the Sum of the Largest Eigenvalues of a Symmetric Matrix', SIAM Journal on Matrix Analysis and Applications, 13, pp. 41 - 45, http://dx.doi.org/10.1137/0613006

Journal articles | 1990

Osborne MR; Womersley RS, 1990, 'Strong uniqueness in sequential linear programming', The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 31, pp. 379 - 384, http://dx.doi.org/10.1017/s0334270000006731

Journal articles | 1988

Overton ML; Womersley RS, 1988, 'On Minimizing the Special Radius of a Nonsymmetric Matrix Function: Optimality Conditions and Duality Theory', SIAM Journal on Matrix Analysis and Applications, 9, pp. 473 - 498, http://dx.doi.org/10.1137/0609040

Journal articles | 1986

Osborne MR; Pruess SA; Womersley RS, 1986, 'Concise representation of generalised gradients', The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 28, pp. 57 - 74, http://dx.doi.org/10.1017/s0334270000005191

Journal articles | 1986

Womersley RS; Fletcher R, 1986, 'An algorithm for composite nonsmooth optimization problems', Journal of Optimization Theory and Applications, 48, pp. 493 - 523, http://dx.doi.org/10.1007/BF00940574

Journal articles | 1986

Womersley RS, 1986, 'Censored Discrete Linear $l_1 $ Approximation', SIAM Journal on Scientific and Statistical Computing, 7, pp. 105 - 122, http://dx.doi.org/10.1137/0907008

Journal articles | 1985

Womersley RS, 1985, 'Local properties of algorithms for minimizing nonsmooth composite functions', Mathematical Programming, 32, pp. 69 - 89, http://dx.doi.org/10.1007/BF01585659

Journal articles | 1983

Teo KL, 1983, 'A Control Parametrization Algorithm for Optimal Control Problems Involving Linear Systems and Linear Terminal Inequality Constraints', Numerical Functional Analysis and Optimization, 6, pp. 291 - 313, http://dx.doi.org/10.1080/01630568308816168
Working Papers | 2019

Hamann J; Gia QTL; Sloan IH; Wang YG; Womersley RS, 2019, A New Probe of Gaussianity and Isotropy applied to the CMB Maps, http://dx.doi.org, http://arxiv.org/abs/1911.11442v2

Working Papers | 2018

Gia QTL; Sloan IH; Womersley RS; Wang YG; Le Gia Q, 2018, Sparse Isotropic Regularization for Spherical Harmonic Representations of Random Fields on the Sphere, http://dx.doi.org
Preprints | 2023

Hamann J; Gia QTL; Sloan IH; Womersley RS, 2023, Removing the mask -- reconstructing a scalar field on the sphere from a masked field, http://dx.doi.org/10.1137/23M1603157

Preprints | 2022

Brauchart JS; Grabner PJ; Sloan IH; Womersley RS, 2022, Needlets Liberated, http://arxiv.org/abs/2207.12838v1

Preprints | 2022

Chafaï D; Saff EB; Womersley RS, 2022, Threshold condensation to singular support for a Riesz equilibrium problem, , http://dx.doi.org/10.48550/arxiv.2206.04956

Preprints | 2021

Chafaï D; Saff EB; Womersley RS, 2021, On the solution of a Riesz equilibrium problem and integral identities for special functions, , http://dx.doi.org/10.48550/arxiv.2108.00534

Preprints | 2019

Hamann J; Gia QTL; Sloan IH; Wang YG; Womersley RS, 2019, A New Probe of Gaussianity and Isotropy applied to the CMB Maps, http://dx.doi.org/10.48550/arxiv.1911.11442

Preprints | 2019

Wang YG; Womersley RS; Wu H-T; Yu W-H, 2019, Numerical computation of triangular complex spherical designs with small mesh ratio, , http://dx.doi.org/10.48550/arxiv.1907.13493

Preprints | 2018

Gia QTL; Sloan IH; Womersley RS; Wang YG, 2018, Sparse Isotropic Regularization for Spherical Harmonic Representations of Random Fields on the Sphere, http://dx.doi.org/10.48550/arxiv.1801.03212

Preprints | 2017

Brauchart JS; Dragnev PD; Saff EB; Womersley RS, 2017, Logarithmic and Riesz Equilibrium for Multiple Sources on the Sphere --- the Exceptional Case, , http://dx.doi.org/10.48550/arxiv.1706.09346

Preprints | 2015

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://dx.doi.org/10.48550/arxiv.1512.07470

Preprints | 2015

Wang YG; Gia QTL; Sloan IH; Womersley RS, 2015, Fully discrete needlet approximation on the sphere, http://dx.doi.org/10.48550/arxiv.1502.05806

Preprints | 2015

Wang YG; Sloan IH; Womersley RS, 2015, Riemann localisation on the sphere, http://dx.doi.org/10.48550/arxiv.1510.06834

Preprints | 2014

Brauchart JS; Dick J; Saff EB; Sloan IH; Wang YG; Womersley RS, 2014, Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces, http://dx.doi.org/10.48550/arxiv.1407.8311

Preprints | 2012

Chernih A; Sloan IH; Womersley RS, 2012, Wendland functions with increasing smoothness converge to a Gaussian, http://dx.doi.org/10.48550/arxiv.1203.5696

Conference Papers | 2002

Sloan IH; Womersley RS, 2002, 'The uniform error of hyperinterpolation on the sphere', in 3rd International conference on multivariate approximation theory, Witten-Bommerholz, Germany, presented at 5th International Conference on Multivariate Approximation, Witten-Bommerholz, Germany, 22 September 2002 - 27 September 2002

Conference Papers | 1999

Sloan IH; Womersley RS, 1999, 'The search for good polynomial interpolation points on the sphere', in Griffiths DF; Watson GA (ed.), 18th Dundee Biennial Conference on Numerical Analysis, University of Dundee, pp. 211 - 229, presented at 18th Dundee Biennial Conference on Numerical Analysis, University of Dundee, 29 June 1999 - 02 July 1999

Conference Papers | 1995

Womersley RS; Lau YK, 1995, 'Portfolio optimisation problems', in Computational Techniques and Applications: Proceedings, Computational Techniques and Applications: CTAC 1995, Singapore, presented at Computational Techniques and Applications: CTAC 1995, Singapore, 11 July 1995 - 14 July 1995

Conference Papers | 1994

Chen X; Womersley RS, 1994, 'A parallel inexact Newton method for stochastic programs with recourse', in Annals of Operations Research, Kluwer Academic Publ, Dordrecht, Netherlands, pp. 113 - 141, presented at IFIP Workshop, Lillehammer, Norway, http://dx.doi.org/10.1007/BF02187643

My research is in the development and application of computational methods for optimization problems, computational mathematics in general, but especially applied to problems of approximation and numerical integration on the sphere, high performance computing and problems in computational finance, such as calibration of financial models to market data.

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Associate Professor Robert Womersley