Dr Joab Winkler

PhD

School of Computer Science

Reader

Course Director for MSc Artificial Intelligence

Member of the Machine Learning research group

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Profile picture of Joab Winkler profile photo
j.r.winkler@sheffield.ac.uk
+44 114 222 1834
Regent Court (DCS)

Full contact details

Dr Joab Winkler
School of Computer Science
Regent Court (DCS)
211 Portobello
Sheffield
S1 4DP
Profile

Joab Winkler is a Reader in The Department of Computer Science at The University of Sheffield. He obtained his undergraduate and PhD degrees at Imperial College London and University College London, respectively. He worked for a few years in industry, before returning to university to conduct research into algebraic and numerical properties of curves and surfaces in computer-aided design systems. He has extended this interest in numerical methods to work on blind image deconvolution, optical flow and neural networks. More details are in the section 'Research interests'.

Research interests

Joab Winkler’s main research interest is the algebraic and numerical properties of curves and surfaces in computer-aided design systems. Most of this work has been performed using resultant matrices, and this has led him to consider more general issues of robust computations on polynomials that are corrupted by added noise. Examples include the computation of a structured low rank approximation of the Sylvester resultant matrix, the deconvolution of two polynomials and the determination of an approximate greatest common divisor of two polynomials.

He has developed a polynomial root solver for the determination of multiple roots of the theoretically exact form of a polynomial, when the coefficients of the given polynomial are corrupted by added noise. He has applied the methods used in this work on polynomials to the deblurring of an image when the point spread function is unknown and must therefore be computed. This is a difficult problem because it is necessary to determine the rank of a matrix whose entries are subject to error. This is one of the most difficult problems in linear algebra.

He has also considered numerical and computational issues in optical flow, which is an important problem in computer vision, in order to identify problems that arise in two commonly used algorithms. 

More recently, he has started work on numerical properties of echo state networks, which are one form of a neural network. 

Publications

Books

  • Winkler J, Lawrence N & Niranjan M (2005) Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics): Preface.

Journal articles

  • Winkler JR & Mitrouli M (2025) . Communications in Statistics - Theory and Methods.
  • Lakshmi MV & Winkler J (2025) . Applied Numerical Mathematics, 208(Part A), 297-309.
  • Winkler JR (2024) . Electronics, 13(5).
  • Winkler J, Mitrouli M & Koukouvinos C (2022) . Journal of Computational and Applied Mathematics, 404.
  • Bourne M, Winkler J & Yi S (2021) . Applied Numerical Mathematics, 166, 348-368.
  • Bourne M, Winkler JR & Su Y (2021) . Journal of Computational and Applied Mathematics, 390.
  • Bourne M, Winkler JR & Su Y (2020) . Journal of Computational and Applied Mathematics, 373.
  • Winkler JR & Mitrouli M (2020) . Journal of Computational and Applied Mathematics, 373.
  • Bourne M, Winkler J & Su Y (2020) . SIAM Journal on Scientific Computing, 42(1), A452-A476.
  • Winkler JR & Halawani H (2018) . Journal of Mathematical Imaging and Vision, 60(8), 1284-1305.
  • Bourne M, Winkler JR & Su Y (2017) . Journal of Computational and Applied Mathematics, 320, 221-241.
  • Winkler JR, Bourne M & Yi S (2016) . Applied Numerical Mathematics, 111, 17-35.
  • Winkler JR (2014) . Journal of Computational and Applied Mathematics, 272, 449-467.
  • Winkler JR & Yang N (2014) . Computer Aided Geometric Design.
  • Winkler JR & Yang N (2013) . Computer Aided Geometric Design, 30(4), 410-429.
  • Winkler JR & Hasan M (2013) . Journal of Computational and Applied Mathematics, 237(1), 253-268.
  • Winkler JR, Lao X & Hasan M (2012) The computation of multiple roots of a polynomial. Journal of Computational and Applied Mathematics.
  • Winkler JR, Hasan M & Lao X (2012) . Calcolo, 49(4), 241-267.
  • Winkler JR & Lao X (2011) . J COMPUT APPL MATH, 235(6), 1587-1603.
  • Winkler JR & Hasan M (2010) . J COMPUT APPL MATH, 234(12), 3226-3242.
  • Winkler JR (2008) . COMPUT AIDED GEOM D, 25(7), 529-541.
  • Winkler JR & Allan JD (2008) . J COMPUT APPL MATH, 215(1), 1-13.
  • Winkler JR & Allan JD (2008) STRUCTURED LOW RANK APPROXIMATIONS OF THE SYLVESTER RESULTANT MATRIX FOR APPROXIMATE GCDS OF BERNSTEIN BASIS POLYNOMIALS. ELECTRON T NUMER ANA, 31, 141-155.
  • Winkler JR (2006) . SIAM J SCI COMPUT, 28(4), 1420-1436.
  • Winkler JR (2006) . J COMPUT APPL MATH, 191(1), 32-49.
  • Winkler JR (2005) . Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 3604 LNCS, 413-433.
  • Bini DA, Gemignani L & Winkler JR (2005) . NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 12(8), 685-698.
  • Winkler JR (2004) . APPL NUMER MATH, 48(1), 113-126.
  • Winkler JR (2003) . Linear Algebra and Its Applications, 362, 153-175.
  • Winkler JR (2003) A statistical analysis of the numerical condition of multiple roots of polynomials. COMPUT MATH APPL, 45(1-3), 9-24.
  • Rees JM, Staszewski WJ & Winkler JR (2001) Case study of a wave event in the stable atmospheric boundary layer overlying an Antarctic Ice Shelf using the orthogonal wavelet transform. DYNAMICS OF ATMOSPHERES AND OCEANS, 34(2-4), 245-261.
  • Winkler JR (2001) Condition numbers of a nearly singular simple root of a polynomial. APPL NUMER MATH, 38(3), 275-285.
  • Winkler JR (2001) A note on the backward error of the roots of polynomials.. Neural Parallel Sci. Comput., 9, 91-96.
  • Winkler JR (2001) . International Journal of Computer Mathematics, 77(4), 583-602.
  • Winkler JR (2000) A resultant matrix for scaled Bernstein polynomials. LINEAR ALGEBRA APPL, 319(1-3), 179-191.
  • Winkler JR (1999) Backward error analysis of the roots of polynomials. Neural, Parallel and Scientific Computations, 7, 463-486.
  • Winkler JR (1997) An ill-conditioned problem in computer aided geometric design. Neural, Parallel & Scientific Computations, 5(1-2), 179-200.
  • Winkler JR (1997) Polynomial basis conversion made stable by truncated singular value decomposition. APPL MATH MODEL, 21(9), 557-568.
  • Winkler JR (1997) Tikhonov regularisation in standard form for polynomial basis conversion. APPL MATH MODEL, 21(10), 651-662.
  • Winkler JR (1996) Singular projective transformation matrices. APPL MATH MODEL, 20(10), 771-778.
  • WINKLER JR & DAVIES JB (1986) ACCURATE FIELD ANALYSIS OF THE PROPAGATION OF ELASTIC-WAVES THROUGH AN ACOUSTIC MICROSCOPE .1. THEORY. IEEE T ULTRASON FERR, 33(6), 644-656.
  • WINKLER JR & DAVIES JB (1986) ACCURATE FIELD ANALYSIS OF THE PROPAGATION OF ELASTIC-WAVES THROUGH AN ACOUSTIC MICROSCOPE .2. RESULTS. IEEE T ULTRASON FERR, 33(6), 657-668.
  • WINKLER JR & DAVIES JB (1984) ELIMINATION OF SPURIOUS MODES IN FINITE-ELEMENT ANALYSIS. J COMPUT PHYS, 56(1), 1-14.
  • Lu Y & Winkler J () . Physica Scripta.
  • Winkler JR () . Linear Algebra and its Applications .

Conference proceedings

  • Alkhaldi N & Winkler JR (2015) . 2015 IEEE International Conference on Image Processing (ICIP) (pp 784-788). Quebec City, Canada, 27 September 2015 - 27 September 2015.
  • Alkhaldi N & Winkler J (2015) . 2015 IEEE International Conference on Image Processing (ICIP) (pp 784-788), 27 September 2015 - 30 September 2015.
  • Winkler JR (2015) . 8th International Conference on Curves and Surfaces (pp 461-490). Switzerland, 12 June 2014 - 18 June 2014.
  • Winkler JR (2015) (pp 461-490)
  • Winkler JR, Martin, R & Sabin, M (2007) . Springer (LNCS 4647), Vol. 4647. Sheffield, 4 September 2007 - 7 September 2007.
  • Winkler JR (2007) Condition numbers and least squares regression. Mathematics of Surfaces XII, Proceedings, Vol. 4647 (pp 480-493)
  • Winkler JR (2006) Structure Preserving methods for the computation of approximate GCDs of Berstein polynomials. 6th International Conference on Curves and Surfaces (pp 11-20). Avignon, France, 29 June 2006 - 5 July 2006.
  • Samani A, Winkler J & Niranjan M (2006) Automatic face recognition using stereo images. 2006 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING, VOLS 1-13 (pp 5771-5774)
  • Winkler JR (2005) A comparison of condition numbers for the full rank least squares problem. DETERMINISTIC AND STATISTICAL METHODS IN MACHINE LEARNING, Vol. 3635 (pp 296-318)
  • (2005) Deterministic and Statistical Methods in Machine Learning, First International Workshop, Sheffield, UK, September 7-10, 2004, Revised Lectures. Deterministic and Statistical Methods in Machine Learning, Vol. 3635
  • Winkler JR (2005) Numerical and algebraic properties of Bernstein basis resultant matrices. COMPUTATIONAL METHODS FOR ALGEBRAIC SPLINE SURFACES (pp 107-118)
  • Winkler JR & Goldman RN (2003) The Sylvester resultant matrix for Bernstein polynomials. Curve and Surface Fitting: Saint-Malo 2002 (pp 407-416). Saint-Malo, 2002 - 2002.
  • Winkler JR & Niranjan, M (2002) Uncertainty in Geometric Computations. Uncertainty in Geometric Computations. Sheffield, 5 July 2001 - 6 July 2001.
  • Winkler JR (2002) Properties of the companion matrix resultant for Bernstein polynomials. UNCERTAINTY IN GEOMETRIC COMPUTATIONS, Vol. 704 (pp 185-198)
  • Winkler JR (2001) Computational experiments with resultants for scaled Bernstein polynomials. MATHEMATICAL METHODS FOR CURVES AND SURFACES: OSLO 2000 (pp 535-544)
  • Winkler JR & Ragozin DL (2000) A class of Bernstein polynomials that satisfy Descartes' rule of signs exactly. MATHEMATICS OF SURFACES IX (pp 424-437)
  • Winkler JR () The numerical condition of roots of polynomials in Bernstein form. Proceedings of the 8th IMA Conference on The Mathematics of Surfaces (pp 265-280). Birmingham, 31 August 1998 - 2 September 1998.
  • Winkler JR () Numerically stable conversion between the Bezier and B-spline forms of a curve. Curves and Surfaces with Applications in CAGD (pp 465-472). Chamonix, 30 June 1997.
  • Winkler JR () The sensitivity of linear algebraic equations. 5th SIAM Conference on Applied Linear Algebra. Snowbird, Utah, USA, 15 June 1994 - 18 June 1994.
Grants
  • Sparse linear models: , EPSRC, 09/2022 - 07/2023, £79,384, as PI
  • Travel Grant, EPSRC, 07/2001 to 08/2001, £1,430, as PI
  • Tensor Tomography for the Three Dimensional Photoelasticity, EPSRC, 11/2002 to 04/2006, £38,818, as PI
  • Robust Computations in Geometric Modelling, EPSRC, 02/2005 to 01/2008, £71,785, as PI
  • Travel Grant, EPSRC, 10/2005 to 01/2006, £4,100, as PI
  • Polynomials and geometric modelling, ROYAL ACADEMY OF ENGINEERING (THE), 01/2010 to 12/2012, £23,613, as PI
Professional activities and memberships
  • Awarded an EPSRC Advanced Research Fellowship (1995)
  • Co-organiser of a workshop, supported by the EPSRC, on The Representation and Management of Uncertainty in Geometric Computations (2001)
  • Co-organiser of The Sheffield Machine Learning Workshop, supported by the EPSRC (2004)
  • Organised the Summer School, supported by the EPSRC, Solving Polynomial Equations and Structured Matrix Methods for Approximate GCD Computations (2007)
  • Awarded a Global Research Award by The Royal Academy of Engineering (2010-2011)
  • Co-organiser of a conference in Kalamata, Greece on structured methods in numerical linear and multilinear algebra (2014)

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