Prof G.A. Watson FIMA, FRSE
- Alistair Watson
- Emeritus Professor
- Division of Mathematics
- University of Dundee
- Dundee DD1 4HN
- 01382 384472
- 01382 385516
- Personal Homepage:
- Please visit my homepage
I am generally interested in finding good algorithms for solving problems which arise in the approximation of functions or data. My main focus has been on problems of best approximation, which involve the minimization of a norm. This sometimes leads me into an investigation of more theoretical aspects of approximation problems. Also, approximation problems can be interpreted as examples of optimization problems or even as examples of problems in linear algebra. Therefore, I am also interested in these areas, in so far as they relate to approximation problems.
- Numerical Analysis
- Numerical methods for data fitting problems
- Orthogonal and non-orthogonal distance regression (PhD Students: A. Atieg, graduated 2005, I. Al-Subaihi,graduated 2006).
- Approximation Theory
- Simultaneous approximation
- Characterization and uniqueness results
- 2007 Numerical Analysis Conference, 26 - 29 June, 2007, Dundee.
- 2007 International Conference of Numerical Analysis and Applied Mathematics,
16-20 September, 2007, Corfu, Greece.
- The Birth of Numerical Analysis, 29 - 30 October, 2007, Leuven, Belgium.
- 2006 Scottish Computational Mathematics Symposium,
14 September, 2006, Heriot-Watt.
- 2005 Numerical Analysis Conference, 28 June - 1 July, 2005, Dundee.
- 2005 Fox Prize Meeting, 27 June, 2005, Dundee.
- Member of Editorial Board: Communications in Applied Analysis,
International Journal of Pure and Applied Mathematics,
Applied Numerical Analysis
and Computational Mathematics .
- Former Editor: IMA Journal of Numerical Analysis, Member of the Editorial Board: SIAM Journal on Matrix Analysis and Applications, Annals of Numerical Mathematics, Proceedings of the Edinburgh Mathematical Society.
Recent Publications and Papers:
- Some robust methods for fitting parametrically defined curves and surfaces to measured data , in Advanced Mathematical and Computational Tools in Metrology IV, Eds P Ciarlini, A B Forbes, F Pavese and D Richter,
Series on Advances in Mathematics for Applied Sciences, Volume 53,
World Scientific, Singapore, pp. 256--272 (2000).
- Algorithms for computing the distance to instability , in Proceedings of the Fourth International Conference on Difference Equations, Poznan, Poland, eds S Elaydi, G Ladas, J Popenda and J Rakowski, Gordon and Breach Science Publishers, Amsterdam, pp. 401--412 (2000).
- Least squares fitting of parametric surfaces to measured data,, ANZIAM J 42 (E), pp. C68--C95 (2000).
- Solving data fitting problems in lp norms with bounded uncertainties in the data , in Numerical Analysis 1999, Chapman and Hall/CRC Research Notes in Mathematics 420, eds D F Griffiths and G A Watson, pp. 249--265 (2000).
- Numerical Analysis 1999 (Proceedings of Dundee Conference), ed. (with D F Griffiths) Chapman and Hall/CRC Research Notes in Mathematics 420 (2000).
- Approximation in Normed Linear Spaces (A Historical Survey of Numerical Methods), Journal of Computational and Applied Mathematics 121, pp. 1--36 (2000).
- On nonlinear coapproximation in Banach spaces (with Chong Li and Renxing Ni), J of Approx Th and its Appl 17, 54--63(2001).
- Implicit surface fitting using directional constraints, (with M Gulliksson
and I Soderkvist), BIT 41, pp. 331-344 (2001).
- Data fitting problems with bounded uncertainties in the data, SIAM J Matrix Analysis and Applications 22, pp. 1274--1293 (2001).
- The limit of best generalized peak norm approximations, (with Chong Li), J Math Anal and Appl 263, pp. 683--694 (2001)
- Robust solutions to linear approximation problems under ellipsoidal uncertainty, in Total Least Squares and Errors-in-Variables Modeling: Analysis, Algorithms and Applications, eds S van Huffel and P Lemmerling, Kluwer, pp. 213--222 (2002).
- On the Gauss-Newton method for l_1 orthogonal distance regression, IMA J Num Anal 22, pp. 345--357 (2002).
- Some problems in orthogonal distance and non-orthogonal distance regression,
Proceedings of Algorithms for Approximation IV , pp 294--302 (2002).
- Incorporating angular information into parametric models, BIT 42, pp 867--878 (2002).
- On the linear statistical relationship Metrika 57, pp 105--114 (2003).
- On a class of methods for fitting a curve or surface to data by minimizing the sum of squares of orthogonal distances, (with A. Atieg), Journal of Computational and Applied Mathematics 158, pp 277--296 (2003).
- Decomposition and descent directions for norms, International Journal of Pure and Applied Mathematics 9, pp. 345--358 (2003).
- On nonlinear simultaneous Chebyshev approximation problems (with Chong Li), J Math Anal and Appl 288, pp. 167--181 (2003).
- Robust solutions to a general class of approximation problems, SIAM J Sci Comp 25, pp. 1448--1460 (2004).
- The $l_1$ oblique Procrustes problem (with N. T. Trendafilov),
Statistics and Computing 14, pp. 39--51 (2004).
- Fitting circular arcs by orthogonal distance regression (with A. Atieg), Applied Numerical Analysis and Computational Mathematics 1, pp. 66--76 (2004).
- Use of l_p norms in fitting curves and surfaces to data (with A. Atieg), Australian and New Zealand Industrial and Applied Mathematics Journal 45 (E), pp. C187--C200 (2004).
- Incomplete orthogonal distance regression (with A. Atieg), BIT 44, pp.619--629 (2004).
- The use of the $l_1$ and $l_\infty$ norms in fitting parametric curves and surfaces to data (with I. Al-Subaihi), Applied Numerical Analysis and Computational Mathematics 1, pp. 363--376 (2004).
- Fitting parametric curves and surfaces by $l_\infty$ distance regression (with I. Al-Subaihi), BIT 45, pp. 443--461 (2005).
- Algebraic fitting of quadric surfaces to data (with I. Al-Subaihi), Communications in Applied Analysis 9, pp. 539--548 (2005).
- An algorithm for matching point sets using the $l_1$ norm (with I. Al-Subaihi), Numerical Algorithms 41, pp. 203--217 (2006).
- Computing Helmert transformations, Journal of Computational and Applied Mathematics 197, pp. 387--395 (2006).
- A History of the Dundee Numerical Analysis Conferences, Mathematics Today 42, pp. 126--128 (2006).
- Fitting enclosing cylinders to data in $R^n$,
Numerical Algorithms 43, pp. 189--196 (2006).
- A Levenberg-Marquardt method for estimating polygonal regions, Journal of Computational and Applied Mathematics 208, pp. 331--340 (2007).
- Robust solutions to linear data fitting problems,
Proceedings of International Confeence on Numerical Analysis and Applied
Mathematics, AIP Conference Proceedings 936, ed. T. E. Simos,
G. Psihoyios and Ch. Tsitouras, pp. 35--38 (2007).
- Robust counterparts of errors-in-variables problems, Computational Statistics and Data Analysis 52, pp. 1080--1089 (2007).
- The history and development of numerical analysis in Scotland: a personal perspective, in The Birth of Numerical Analysis, eds A Bultheel and R Cools, World Scientific (2010).