Refereed Journal Publications

Constructing strong linearizations of matrix polynomials expressed in the Chebyshev bases MIMS preprint

Piers W. Lawrence and Javier Perez, SIAM Journal on Matrix Analysis and Applications, 38(3), pp. 683-709.

Backward error analysis of polynomial eigenvalue problems solved by linearization

Piers W. Lawrence, Marc Van Barel, and Paul Van Dooren, SIAM Journal on Matrix Analysis and Applications, 37(1) (2016), pp. 123-144.

Backward Error of Polynomial Eigenvalue Problems Solved by Linearization of Lagrange Interpolants

Piers W. Lawrence and Robert M. Corless, SIAM Journal on Matrix Analysis and Applications, 36(4) (2015), pp. 1425-1442.

Stability of rootfinding for barycentric Lagrange interpolants

Piers W. Lawrence and Robert M. Corless, Numerical Algorithms, 65(3) (2014), pp. 447-464.

Fast reduction of generalized companion matrix pairs for barycentric Lagrange interpolants

Piers W. Lawrence, SIAM Journal on Matrix Analysis and Applications, 34(3) (2013), pp. 1277-1300.

The largest roots of the Mandelbrot polynomials

Robert M. Corless and Piers W. Lawrence. In D. Bailey, H.H. Bauschke, P. Borwein, F. Garvan, M. Thera, J. Vanderwerff and H. Wolkowicz, editors, Computational and Analytical Mathematics, vol. 50 of Springer Proceedings in Mathematics & Statistics, Springer New York, 2013, pp. 305-324.

Algorithm 917: Complex Double-Precision Evaluation of the Wright ω function Implementation

Piers W. Lawrence, Robert M. Corless and David J. Jeffrey. ACM Transactions on Mathematical Software, 38(3) (2012): 20.

Numerical Stability of Barycentric Hermite Rootfinding

Piers W. Lawrence and Robert M. Corless. In Marc Moreno Maza, editor, Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation, ACM, 2011, pp. 147-148.

The Impact of Parameter Identification Methods on Drug Therapy Control in an Intensive Care Unit

C.E. Hann, J.G. Chase, M.F. Ypma, J. Elfring, N.H.M. Nor, P.W. Lawrence and G.M. Shaw. The Open Medical Informatics Journal, 2 (2008), pp. 92-104.

Conference Presentations

Structured backward error analysis of eigenvalue problems solved by linearization

Piers Lawrence, Marc Van Barel, and Paul Van Dooren, presented at the Mat Triad 2015, conference on Matrix Analysis and its Applications, Coimbra, Portugal, 7-11 September 2015.

Backward error of polynomial eigenvalue problems solved by Linearization

Piers W. Lawrence, Marc Van Barel, Paul Van Dooren, presented at the GAMM 86th Annual Meeting of the International Association of Applied Mathematics and Mechanics, Lecce, Italy, 23-27 March 2015.

On the stability of polynomial eigenvalue problems solved via linearization

Piers Lawrence, Marc Van Barel, and Paul Van Dooren, presented at the 10th International Workshop on Accurate Solution of Eigenvalue Problems, Dubrovnik, Croatia, 2-5 June 2014.

Linearizations for Interpolation Bases

Piers Lawrence, presented at the Manchester Workshop on Nonlinear Eigenvalue Problems, Manchester, UK, 2014.

Rootfinding for Polynomial and Rational Interpolants

Piers Lawrence, presented at 3rd Dolomites Workshop on Constructive Approximation and Applications (DWCAA12), Alba di Canazei, Italy.

Eigenstructure of an Arrowhead Matrix Pencil

Piers Lawrence and Rob Corless, presented at ICIAM 2011, Vancouver, Canada.

Numerical Stability of Barycentric Hermite Rootfinding

Piers Lawrence and Rob Corless, presented at Symbolic Numeric Computation 2011, San Jose, USA.

On the Stability of Barycentric Hermite Rootfinding

Piers Lawrence and Rob Corless, presented at SONAD 2011, McMaster University, Hamilton, Canada.

Event handling with barycentric Hermite interpolation

Piers Lawrence, Rob Corless, Ned Nedialkov, presented at CAIMS*SCMAI 2010, St John’s, Canada.

Seminar Presentations

Fiedler-like linearizations for polynomial matrices

Joint work with Paul Van Dooren, Froilan Dopico, and Javier Perez, presented at the Department of Computer Science, KU Leuven, Leuven, Belgium, November 2015.

Semi-practical algorithms for computing the periodic points of the Mandelbrot set

presented at the Department of Mathematics, KU Leuven, Leuven, Belgium.

Barycentric Lagrange Interpolation and Rootfinding

presented at the Department of Mathematical Engineering, UC Louvain, Louvain-la-Neuve, Belgium, October 2013.

Posters

Linearizations for interpolation bases

Piers Lawrence, Marc Van Barel, and Paul Van Dooren, presented at the IAP DYSCO Study Day: Dynamical systems, control and optimization, 2014, University of Namur, Namur, Belgium.

Mandelbrot Polynomials and Matrices

Piers Lawrence and Rob Corless, presented at the IAP DYSCO Study Day: Dynamical systems, control and optimization, 2013, Palais des Académies, Brussels, Belgium.

Mandelbrot Polynomials and Matrices

Piers Lawrence and Rob Corless, presented at the East Coast Computer Algebra Day (ECCAD) 2012, Oakland University, Rochester, Michigan, USA.

Computing Roots of Mandelbrot Polynomials

Piers Lawrence and Rob Corless, presented at the East Coast Computer Algebra Day (ECCAD) 2011, The University of Waterloo, Waterloo, Canada.

Technical Reports

Structured backward error analysis of polynomial eigenvalue problems solved by linearization

Lawrence, Piers W., Van Barel, Marc, and Van Dooren, Paul
TW Reports, TW661, Department of Computer Science, KU Leuven, June 2015.

Backward error of polynomial eigenvalue problems solved by linearization of Lagrange interpolants

Lawrence, Piers W., and Corless, Robert M.
TW Reports, TW655, Department of Computer Science, KU Leuven, February 2015.

A Mechatronically Measurable Double Pendulum for Machine Interval Experiments

Piers Lawrence, Michael Stuart, Richard Brown, Warwick Tucker and Raazesh Sainudiin.
Indian Statistical Institute Technical Report, isibang/ms/2010/11, October 25, 2010

Theses

Eigenvalue Methods for Interpolation Bases

Piers W. Lawrence, PhD thesis, Department of Applied Mathematics, The University of Western Ontario, 2013.

Parameter estimation techniques for insulin-glucose models.

Piers W. Lawrence, Honours Thesis, Department of Mathematics and Statistics, University of Canterbury, 2008

In Preparation

Block Kronecker Linearizations of Matrix Polynomials and their Backward Errors

Froilán M. Dopico, Piers W. Lawrence, Paul Van Dooren, and Javier Pérez (submitted, May 2016)

Linearization of Lagrange polynomials in a Fiedler-like way

Piers W. Lawrence and Leonardo Robol

Development of an $\mathbb{L}_1$-like pencil Space for matrix polynomials in Lagrange bases

Piers W. Lawrence, D. Steven Mackey, and Vasilije Perović

Polynomial roots from generalized eigenvalues

Piers W. Lawrence, Froilán M. Dopico, Paul Van Dooren, and Javier Pérez

Mandelbrot Polynomials and Matrices

P.W. Lawrence, R.M. Corless, and D.J. Jeffrey