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Usevich, Konstantin, Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X, Dreesen, Philippe and Markovsky, Ivan 2025. Structured nuclear norm matrix completion: Guaranteeing exact recovery via block-column scaling. Numerical Linear Algebra with Applications 32 (4) , e70031. 10.1002/nla.70031
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Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X and Usevich, Konstantin 2025. Low-rank approximations in statistics. Lovric, Miodrag, ed. International Encyclopedia of Statistical Science, Springer, pp. 1398-1400. (10.1007/978-3-662-69359-9_338)

Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X, Knight, Vincent ORCID: https://orcid.org/0000-0002-4245-0638, Smith, Kendal and Wilde, Henry 2025. Optimising healthcare queues: a case study on chronic respiratory illness. IMA Journal of Management Mathematics 36 (2) , pp. 255-274. 10.1093/imaman/dpaf002
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Knight, Vincent ORCID: https://orcid.org/0000-0002-4245-0638, Harper, Marc, Glynatsi, Nikoleta E. and Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X 2024. Recognising and evaluating the effectiveness of extortion in the Iterated Prisoner’s Dilemma. PLoS ONE 19 (7) , e0304641. 10.1371/journal.pone.0304641
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Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X, O'Riordan, Emily and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2023. Polynomial whitening for high-dimensional data. Computational Statistics 38 , pp. 1427-1461. 10.1007/s00180-022-01277-6
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Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X, Knight, Vincent ORCID: https://orcid.org/0000-0002-4245-0638 and Wilde, Henry 2023. A novel initialisation based on hospital-resident assignment for the k-modes algorithm. Soft Computing 27 , pp. 9441-9457. 10.1007/s00500-023-08407-2
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Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X and Usevich, Konstantin 2023. Hankel low-rank approximation and completion in time series analysis and forecasting: a brief review. Statistics and Its Interface 16 (2) , pp. 287-303. 10.4310/22-SII735
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Gillard, J. W. ORCID: https://orcid.org/0000-0001-9166-298X and Usevich, K. 2022. Matrix optimization problems in statistics. Pardalos, Panos M. and Prokopyev, Oleg A., eds. Encyclopedia of Optimization, Springer, [n/a]. (10.1007/978-3-030-54621-2_771-1)

Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X, O'Riordan, Emily and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2022. Simplicial and minimal-variance distances in multivariate data analysis. Journal of Statistical Theory and Practice 16 , 9. 10.1007/s42519-021-00227-7
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Zilinskas, Antanas, Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X, Scammell, Megan and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2021. Multistart with early termination of descents. Journal of Global Optimization 79 , pp. 447-462. 10.1007/s10898-019-00814-w
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Wilde, Henry, Knight, Vincent ORCID: https://orcid.org/0000-0002-4245-0638 and Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X 2020. Evolutionary dataset optimisation: learning algorithm quality through evolution. Applied Intelligence 50 , pp. 1172-1191. 10.1007/s10489-019-01592-4
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Wilde, Henry, Knight, Vincent ORCID: https://orcid.org/0000-0002-4245-0638 and Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X 2020. Matching: a Python library for solving matching games. Journal of Open Source Software 5 (48) , 2169. 10.21105/joss.02169
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Ford, Shauna, Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X and Pugh, Mathew ORCID: https://orcid.org/0000-0001-9045-3713 2019. Creating a taxonomy of mathematical errors for undergraduate mathematics. MSOR Connections 18 (1) , pp. 37-45. 10.21100/msor.v18i1
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Dewart, Neil and Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X 2019. Using Bradley-Terry models to analyse test match cricket. IMA Journal of Management Mathematics 30 (2) , pp. 187-207. 10.1093/imaman/dpx013
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Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X and Usevich, Konstantin 2018. Structured low-rank matrix completion for forecasting in time series analysis. International Journal of Forecasting 34 (4) , pp. 582-597. 10.1016/j.ijforecast.2018.03.008
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Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2018. Optimal directional statistic for general regression. Statistics and Probability Letters 143 , p. 74. 10.1016/j.spl.2018.07.025
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Hurt, Lisa ORCID: https://orcid.org/0000-0002-2741-5383, Langley, Kate ORCID: https://orcid.org/0000-0002-2033-2657, North, Kate, Southern, Alex, Copeland, Lauren ORCID: https://orcid.org/0000-0003-0387-9607, Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X and Williams, Sharon J 2018. Understanding and improving the care pathway for children with autism. International Journal of Health Care Quality Assurance 32 (1) , pp. 208-223. 10.1108/IJHCQA-08-2017-0153
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Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2018. Optimal estimation of direction in regression models with large number of parameters. Applied Mathematics and Computation 318 , pp. 281-289. 10.1016/j.amc.2017.05.050
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Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X 2017. An initial analysis and reflection of the metrics used in the Teaching Excellence Framework in the UK. Perspectives: Policy and Practice in Higher Education 22 (2) , pp. 49-57. 10.1080/13603108.2017.1409669
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Vile, J. L., Gillard, J. W. ORCID: https://orcid.org/0000-0001-9166-298X, Harper, P. R. ORCID: https://orcid.org/0000-0001-7894-4907 and Knight, V. A. ORCID: https://orcid.org/0000-0002-4245-0638 2017. A queueing theoretic approach to set staffing levels in time-dependent dual-class service systems. Decision Sciences 48 (4) , pp. 766-794. 10.1111/deci.12236
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Gillard, J. W. ORCID: https://orcid.org/0000-0001-9166-298X and Kvasov, D. E. 2017. Lipschitz optimization methods for fitting a sum of damped sinusoids to a series of observations. Statistics and Its Interface 10 (1) , pp. 59-70. 10.4310/SII.2017.v10.n1.a6
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Butcher, Holly and Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X 2017. Simple nuclear norm based algorithms for imputing missing data and forecasting in time series. Statistics and Its Interface 10 (1) , pp. 19-25. 10.4310/SII.2017.v10.n1.a2
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Davies, Gareth, Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2016. Comparative study of different penalty functions and algorithms in survey calibration. Comparative Study of Different Penalty Functions and Algorithms in Survey Calibration, Vol. 107. pp. 87-127. (10.1007/978-3-319-29975-4_6)

Gillard, J. W. ORCID: https://orcid.org/0000-0001-9166-298X and Zhigljavsky, A. A. ORCID: https://orcid.org/0000-0003-0630-8279 2016. Weighted norms in subspace-based methods for time series analysis. Numerical Linear Algebra with Applications 23 (5) , pp. 947-967. 10.1002/nla.2062
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Vile, Julie Leanne, Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X, Harper, Paul Robert ORCID: https://orcid.org/0000-0001-7894-4907 and Knight, Vincent Anthony ORCID: https://orcid.org/0000-0002-4245-0638 2016. Time-dependent stochastic methods for managing and scheduling Emergency Medical Services. Operations Research for Health Care 8 , pp. 42-52. 10.1016/j.orhc.2015.07.002
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Evans, Dafydd and Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X 2016. Difference-based methods for truncating the singular value decomposition. Communications in Statistics - Simulation and Computation 45 (3) , pp. 863-879. 10.1080/03610918.2013.875572
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Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X, Knight, Vincent Anthony ORCID: https://orcid.org/0000-0002-4245-0638, Vile, Julie Leanne and Wilson, Robert 2016. Rostering staff at a mathematics support service using a finite-source queueing model. IMA Journal of Management Mathematics 27 (2) , pp. 201-209. 10.1093/imaman/dpu017
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Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2016. Global optimization for structured low rank approximation. Presented at: International Conference of Numerical Analysis and Applied Mathematics 2015, Rhodes, Greece, 22-28 September 2015. AIP Conference Proceedings. , vol.1738 American Institute of Physics, p. 400003. 10.1063/1.4952191
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Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X 2015. Linear time-dependent reference intervals where there is measurement error in the time variable - a parametric approach. Statistical Methods in Medical Research 24 (6) , pp. 788-802. 10.1177/0962280211426617

Gillard, J. W. ORCID: https://orcid.org/0000-0001-9166-298X and Zhigljavsky, A. A. ORCID: https://orcid.org/0000-0003-0630-8279 2015. Stochastic algorithms for solving structured low-rank approximation problems. Communications in Nonlinear Science and Numerical Simulation 21 (1-3) , pp. 70-88. 10.1016/j.cnsns.2014.08.023
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Davies, Gareth P., Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X and Zhigljavsky, Anatoly Alexandrovich ORCID: https://orcid.org/0000-0003-0630-8279 2015. Calibration in survey sampling as an optimization problem. Migdalas, Athanasios and Karakitsiou, Athanasia, eds. Optimization, Control, and Applications in the Information Age, Vol. 130. Springer Proceedings in Mathematics & Statistics, vol. 130. Springer, pp. 67-89. (10.1007/978-3-319-18567-5_4)
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Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X and Knight, Vincent Anthony ORCID: https://orcid.org/0000-0002-4245-0638 2014. Using singular spectrum analysis to obtain staffing level requirements in emergency units. Journal of the Operational Research Society 65 (5) , pp. 735-746. 10.1057/jors.2013.41
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Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X 2014. Method of moments estimation in linear regression with errors in both variables. Communications in Statistics: Theory and Methods 43 (15) , pp. 3208-3222. 10.1080/03610926.2012.698785
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Pickles, T ORCID: https://orcid.org/0000-0001-7743-0234, Playle, R ORCID: https://orcid.org/0000-0002-2989-1092, Hood, K ORCID: https://orcid.org/0000-0002-5268-8631, Gillard, J ORCID: https://orcid.org/0000-0001-9166-298X and Robling, M ORCID: https://orcid.org/0000-0002-1004-036X 2013. Rasch analysis of the PedsQL 3.0 diabetes module. [Abstract]. Trials 14 (S1) , 040. 10.1186/1745-6215-14-S1-O40

Vile, Julie, Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X, Harper, Paul Robert ORCID: https://orcid.org/0000-0001-7894-4907 and Knight, Vincent Anthony ORCID: https://orcid.org/0000-0002-4245-0638 2013. Integrating demand forecasting and workforce planning strategies for emergency medical services. Presented at: Operational Research Applied to Health Services (ORAHS), Istanbul, Turkey, July 2013.

Quinn, Lori ORCID: https://orcid.org/0000-0002-2982-923X, Khalil, Hanan, Dawes, Helen, Fritz, Nora E., Kegelmeyer, Deb, Kloos, Anne D., Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X and Busse, Monica ORCID: https://orcid.org/0000-0002-5331-5909 2013. Reliability and minimal detectable change of physical performance measures in individuals with pre-manifest and manifest Huntington disease. Physical Therapy 93 (7) , pp. 942-956. 10.2522/ptj.20130032

Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X and Zhigljavsky, Anatoly Alexandrovich ORCID: https://orcid.org/0000-0003-0630-8279 2013. Optimization challlenges in the structured low rank approximation problem. Journal of Global Optimization 57 (3) , pp. 733-751. 10.1007/s10898-012-9962-8

Lewis, Rhyd ORCID: https://orcid.org/0000-0003-1046-811X, Thompson, Jonathan Mark, Mumford, Christine Lesley ORCID: https://orcid.org/0000-0002-4514-0272 and Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X 2012. A wide-ranging computational comparison of high-performance graph colouring algorithms. Computers & Operations Research 39 (9) , pp. 1933-1950. 10.1016/j.cor.2011.08.010
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Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X, Robathan, Kirsty J. and Wilson, Robert 2012. Student perception of the effectiveness of mathematics support at Cardiff University. Teaching Mathematics and its Applications 31 (2) , pp. 84-94. 10.1093/teamat/hrs006

Vile, Julie Leanne, Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X, Harper, Paul Robert ORCID: https://orcid.org/0000-0001-7894-4907 and Knight, Vincent Anthony ORCID: https://orcid.org/0000-0002-4245-0638 2012. Predicting ambulance demand using singular spectrum analysis. Journal of the Operational Research Society 63 , pp. 1556-1565. 10.1057/jors.2011.160

Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X 2012. A generalised Box-Cox transformation for the parametric estimation of clinical reference intervals. Journal of Applied Statistics 39 (10) , pp. 2231-2245. 10.1080/02664763.2012.706266

Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X 2011. Asymptotic variance–covariance matrices for the linear structural model. Statistical Methodology 8 (3) , pp. 291-303. 10.1016/j.stamet.2010.12.002

Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X, Robathan, Kirsty Jayne and Wilson, Robert 2011. Measuring the effectiveness of a mathematics support service: an email survey. Teaching Mathematics and its Applications 30 (1) , pp. 43-52. 10.1093/teamat/hrq017

Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X and Zhigljavsky, Anatoly Alexandrovich ORCID: https://orcid.org/0000-0003-0630-8279 2011. Analysis of structured low rank approximation as an optimization problem. Informatica 22 (4) , pp. 489-505.

Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X 2010. An overview of linear structural models. Revstat 8 (1) , pp. 57-80.

Vile, Julie Leanne, Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X, Harper, Paul Robert ORCID: https://orcid.org/0000-0001-7894-4907 and Knight, Vincent Anthony ORCID: https://orcid.org/0000-0002-4245-0638 2010. Forecasting Welsh ambulance demand using singular spectrum analysis. Presented at: 36th International ORAHS conference, Genova, Italy, 18-23 July 2010. Published in: Testi, Angela ed. Operations Research for Patient-Centered Health Care Delivery: Proceedings of the XXXVI International ORAHS Conference. Proceedings of the XXXVI International ORAHS Conference. Economia (5) Milan: Franco Angeli, pp. 196-208.

Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X, Levi, Margaret Louise and Wilson, Robert 2010. Diagnostic testing at UK universities: an e-mail survey. Teaching Mathematics and its Applications 29 (2) , pp. 69-75. 10.1093/teamat/hrq004

Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X 2010. Cadzow's basic algorithm, alternating projections and singular spectrum analysis. Statistics and Its Interface 3 (3) , pp. 333-343. 10.4310/SII.2010.v3.n3.a7

Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X and Iles, Terence Crossley 2009. Methods of fitting straight lines where both variables are subject to measurement error. Current Clinical Pharmacology 4 (3) , pp. 164-171. 10.2174/157488409789375302

Phillips, John, Smith, Michael ORCID: https://orcid.org/0000-0002-4199-3315 and Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X 2009. Do competitive swimmers have altered scapular upward rotation angles compared to non-swimmers? Presented at: 6th All – Wales Conference on Sport and Exercise Medicine and Science, Aberystwyth, UK, 3 July 2009.

Holmes, Anita, Smith, Michael ORCID: https://orcid.org/0000-0002-4199-3315 and Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X 2009. Does scapula position change in the dominant arm of competitive swimmers after a swimming training session? Presented at: 6th All – Wales Conference on Sport and Exercise Medicine and Science, Aberystwyth, UK, 3 July 2009.

Holmes, Anita, Smith, Michael ORCID: https://orcid.org/0000-0002-4199-3315 and Gillard, Jonathan ORCID: https://orcid.org/0000-0001-9166-298X 2009. Does scapula position change in the dominant arm of competitive swimmers after a swimming training session? Presented at: The Association of Chartered Physiotherapists in Sports Medicine Annual Conference, Leeds, UK, 4 September 2009.

Wilson, Robert and Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X 2008. Some problems associated with running a Maths Support Service. Presented at: CETL-MSOR Conference 2008, Lancaster University, Lancaster, UK, 8-9 September 2008. Published in: Green, D. ed. CETL-MSOR Conference 2008 Conference Proceedings. Birmingham: The Maths, Stats & OR Network, pp. 94-99.

Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X 2007. Errors in variables regression: What is the appropriate model? PhD Thesis, Cardiff University.
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