# Papers, Technical reports and Theses

### Refereed Journal Publications

Constructing strong linearizations of matrix polynomials expressed in the Chebyshev bases MIMS preprintPiers W. Lawrence and Javier Perez, *SIAM Journal on Matrix Analysis and Applications,* 38(3), pp. 683-709.

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

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

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

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

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.

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

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.

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 linearizationPiers 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 LinearizationPiers 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 linearizationPiers 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 BasesPiers Lawrence, presented at the Manchester Workshop on Nonlinear Eigenvalue Problems, Manchester, UK, 2014.

Rootfinding for Polynomial and Rational InterpolantsPiers Lawrence, presented at 3rd Dolomites Workshop on Constructive Approximation and Applications (DWCAA12), Alba di Canazei, Italy.

Eigenstructure of an Arrowhead Matrix PencilPiers Lawrence and Rob Corless, presented at ICIAM 2011, Vancouver, Canada.

Numerical Stability of Barycentric Hermite RootfindingPiers Lawrence and Rob Corless, presented at Symbolic Numeric Computation 2011, San Jose, USA.

On the Stability of Barycentric Hermite RootfindingPiers Lawrence and Rob Corless, presented at SONAD 2011, McMaster University, Hamilton, Canada.

Event handling with barycentric Hermite interpolationPiers Lawrence, Rob Corless, Ned Nedialkov, presented at CAIMS*SCMAI 2010, St Johnâ€™s, Canada.

### Seminar Presentations

Fiedler-like linearizations for polynomial matricesJoint 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 setpresented at the Department of Mathematics, KU Leuven, Leuven, Belgium.

Barycentric Lagrange Interpolation and Rootfindingpresented at the Department of Mathematical Engineering, UC Louvain, Louvain-la-Neuve, Belgium, October 2013.

### Posters

Linearizations for interpolation basesPiers 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 MatricesPiers 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 MatricesPiers Lawrence and Rob Corless, presented at the East Coast Computer Algebra Day (ECCAD) 2012, Oakland University, Rochester, Michigan, USA.

Computing Roots of Mandelbrot PolynomialsPiers 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 linearizationLawrence, Piers W., Van Barel, Marc, and Van Dooren, Paul

TW Reports, TW661, Department of Computer Science, KU Leuven, June 2015.

Lawrence, Piers W., and Corless, Robert M.

TW Reports, TW655, Department of Computer Science, KU Leuven, February 2015.

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

Linearization of Lagrange polynomials in a Fiedler-like wayPiers W. Lawrence and Leonardo Robol

Development of an $\mathbb{L}_1$-like pencil Space for matrix polynomials in Lagrange basesPiers W. Lawrence, D. Steven Mackey, and Vasilije Perović

Polynomial roots from generalized eigenvaluesPiers W. Lawrence, Froilán M. Dopico, Paul Van Dooren, and Javier Pérez

Mandelbrot Polynomials and MatricesP.W. Lawrence, R.M. Corless, and D.J. Jeffrey