## Prof John Pryce

### Overview

Telephone: +44(0)29 208 74207

Fax: +44(0)29 208 74199

Extension: 74194

Location: M/0.17

#### Research Interests

Differential Algebraic Equations and the use of Structural Analysis to aid their numerical solution.

Standardisation of Interval Arithmetic.

Theory and use of Automatic Differentiation in numerical computation.

#### Teaching

**Undergraduate - Spring Semester**

MA0111 Elementary Number Theory I

**Postgraduate - Spring Semester**

MAGIC062 Introductory Functional Analysis

#### Recent Significant Publications

J. D. Pryce and G.F. Corliss. Interval arithmetic with containment sets. Computing 78: 251–276, 2006.

J. D. Pryce. A simple structural analysis method for DAEs. BIT, 41(2):364–394, 2001.

N. S. Nedialkov and J. D. Pryce. Solving differential-algebraic equations by Taylor series (III): The DAETS code. JNAIAM, 3(1–2):61–80, 2008. ISSN 17908140.

J. D. Pryce and E.M. Tadjouddine. Fast Automatic Differentiation Jacobians by Compact LU Factorization. SIAM J Sci Comp 30: 1659–1677, 2008.

### Publications

#### Publications in Pure Mathematics

On type F semi-algebras of continuous functions, Quart. J Math. Oxford (2), 16(1965), 65–71.

Weak compactness in locally convex spaces, Proc. Amer. Math. Soc. 17, no. 1 (1966) 148–155.

A counterexample concerning type in semi-algebras of continuous functions, Quart. J Math. Oxford (2), 19 (1968), 9–15.

On the representation and some separation properties of semi-extremal subsets of con- vex sets, Quart. J Math. Oxford (2), 20 (1969), 367–382.

with J. Duncan et al. The numerical index of a normed space, J London Math. Soc. (2), 2 (1970), 481–488.

A device of R.J. Whitley’s applied to pointwise compactness in spaces of continuous functions, Proc. London Math. Soc. (3), 23 (1971), 532–546.

with G. Brown. Stability theorems for wedges, Proc. Edinburgh Math. Soc. 17, no. 3 (1971) 201–214.

An unpleasant set in a non-locally convex vector lattice, Proc. Edinburgh Math. Soc. 18, no. 3 (1973) 229–233.

Non self-determining faces — an example, Math. Scandinavica 33 (1973), 21–22. 10. with D.H. Fremlin. Semi-extremal sets and measure representations, Proc. London Math. Soc. (3), 29 (1974) 502–520.

Textbook. Basic Methods of Linear Functional Analysis, Hutchinson University Li- brary, London (1973), 320pp.

with G.W. Cook & D.F. Kerridge. Estimations of functions of a binomial parameter, Sankhya, Ser. A 36 (1974) 443–448.

#### Publications in Numerical Analysis and Mathematical Software

with M.W. Evans and W.T. Coffey. The effect of dipole-dipole interaction on Zero- THz frequency polarization, Chemical Physics Letters 63 (1979), 133–138.

Roundoff error analysis with fewer tears, Bulletin Inst. Maths & Applics 17 (1981), 40–47.

with J.W. Paine. A stiff ODE solver for an attached processor, Computer Physics Comm 27 (1982), 97–100.

A new measure of relative error for vectors, SIAM J Numer Anal 21 (1984), 202–215. 17. Experiences with writing library software for an attached processor, Software Practice

and Experience 15 (1985) 705–714.

with J.J. Modi. Efficient implementation of Jacobi’s diagonalization method on the

DAP, Numer. Math. 46 (1985) 443–454. 6

Multiplicative error analysis of matrix transformation algorithms, IMA J Numer. Analysis 5 (1985) 437–445.

Error control of phase function shooting methods for Sturm–Liouville problems, IMA J Numerical Analysis 6 (1986) 103–123.

with J.J. Modi. Mobile Jacobi schemes for parallel computation, Comp. & Math. with Applications 12B (1986) 1217–1224.

Error estimation for a class of differential eigenproblems, J Computational Physics 69 (1987) 252–257.

with W.H. Enright. Two Fortran packages for assessing initial value methods, ACM Trans. Math. Software 13(1984) 1–34. The DETEST package, which this describes, is distributed by ACM.

with W. Govaerts. A singular value inequality for block matrices, Linear Algebra and its Applications 125 (1989) 141–148.

On the convergence of iterated remeshing, IMA J Numer. Analysis 9 (1989) 315–335.

with B.M. Brown and V. Kirby. Numerical determination of the Titchmarsh–Weyl m(λ) function and its applications to HELP inequalities, Proc. Roy. Soc. London A 426 (1989) 167–188.

with W. Govaerts. Block elimination with one refinement solves bordered linear sys- tems accurately, BIT 30 (1990) 490–507.

with P.H. Davis and B.R. Stephens. Recent developments in automatic differentiation, in Scientific Software Systems, J.C. Mason and M.G. Cox eds, Chapman and Hall, 1990.

with M. Marletta. A new multi-purpose software package for Schršodinger and Sturm– Liouville computations Comput. Phys. Comm. 62 (1991) 42–52.

with W. Govaerts. Block elimination with iterative refinement for bordered linear systems in Proc. NATO Advanced Scientific Institute, Leuven, Belgium 1988, NATO ASI Ser. F 70, (1991) 513–519.

with B.M. Brown and V.G. Kirby. A numerical method for the determination of the Titchmarsh-Weyl m(λ) coefficient Proc. Roy. Soc. London A 435 (1991) 535–549.

with M. Marletta. Automatic solution of Sturm–Liouville problems using the Pruess method J Comp. Appl. Math. 39 (1992) 57–78.

Methods for adaptive remeshing in one space dimension, in Proc. 4th Internat. Conf. Computational Differential Equations, Benin City, Nigeria, Univ. Ibadan Press 1992.

with W. Govaerts. Mixed block elimination for linear systems with wider borders IMA J Numer. Anal. 13 (1993) 161–180.

Efficient, reliable computation of resonances of the one-dimensional Schršodinger equa- tion J Comput. Physics 112 (1994) 234–246.

Classical and vector Sturm–Liouville problems: recent advances in shooting-type meth- ods and singular-point analysis J Comp. Appl. Math. 50 (1994) 455–470.

Monograph. Numerical Solution of Sturm–Liouville Problems, Oxford University Press. Dec 1993, 325pp, ISBN 019–853–4159.

with M Marletta. LCNO Sturm–Liouville problems: computational difficulties and examples Numerische Mathematik 69 (1995) 303–320.

with A. Harrison & M.P. Lee. Prolog as first programming language in Proc. Internat. Conf. on Software Engineering in Higher Education, Nov 1994. Computer Mathemat- ical Publications, Southampton, UK.

SLDRIVER, a tool for exploring Sturm–Liouville problems and Sturm–Liouville solvers in Spectral Theory and computational methods of Sturm–Liouville problems, 349– 376, (Proceedings 1996 Barratt Lectures, Univ Tennessee at Knoxville), D. Hinton, P. Schaefer (eds). Marcel Dekker Inc., 1997.

with D. Rhodes. Non-linear least squares analysis of pumping test data in Proceedings 10th IAHR-APD Congress, S.C. Lee, K.L. Hiew, S.H. Ong (eds), Vol I (1996) 615–622. National Hydraulic Research Institute, Langkawi, Malaysia.

Solving high-index DAEs by Taylor series, Numerical Algorithms vol 19 (1998) 195– 211. (Proceedings 1997 DAEs Workshop, Grenoble, France.) Baltzer Science Pub- lishers, Amsterdam.

Book Review of Numerical Algorithms with C and Numerical Algorithms with Fortran by Engeln-Mullges and Uhlig, Springer Verlag 1996. In SIAM Reviews vol 40, no. 1 (1998) 171–173.

A test package for Sturm–Liouville solvers and Algorithm 789: SLTSTPAK, a test package for Sturm–Liouville solvers; accompanied by SLTSTPAK and SLDRIVER software. ACM Trans. Math. Software vol 25, no. 1, (1999) 21–57 and 58–69.

with Ned Nedialkov and Ken Jackson. An effective high-order interval method for validating existence and uniqueness for the solution of an IVP for an ODE, Reliable Computing 7, no. 6 (2001) 449–465.

A simple structural analysis method for DAEs, BIT Numerical Mathematics 41, no. 2, (2001) 364–394.

with Shaun Forth and Mohamed Tadjouddine. AD Tools and Prospects for Optimal AD in CFD Flux Jacobian Calculations. In Automatic Differentiation: From Sim- ulation to Optimization, eds. George Corliss, Christele Faure, Andreas Griewank, Laurent Hascoet, and Uwe Naumann. Springer, New York, 2001. Proceedings of AD 2000: 3rd International Conference/Workshop on Automatic Differentiation: From Simulation to Optimization

with Shaun Forth, John Reid and Mohamed Tadjouddine. Performance Issues for Vertex Elimination Methods in Computing Jacobians using Automatic Differentia- tion. In Special Session on Automatic Differentiation and Applications, Proc. Second International Conference on Computational Science, eds. Peter M.A. Sloot et al., Lecture Notes in Computer Science 2330, 1077–1086, Springer, Amsterdam 2002.

with Shaun Forth and Mohamed Tadjouddine. Jacobian Code Generated by Source Transformation and Vertex Elimination can be as Efficient as Hand-Coding. To ap- pear in ACM Trans. Math. Software.

with Nedialko Nedialkov. Solving Differential-Algebraic Equations by Taylor Series (I): Computing Taylor Coefficients. Submitted to BIT Numerical Mathematics, Oc- tober 2003.

#### Published software

The Sturm–Liouville solvers in NAg Fortran Library, Mark 8 to present (1978).

with W.H.Enright. The DETEST Package for performance testing of ODE initial value codes, in ACM Collected Algorithms (1984). Available in NETLIB.

Subroutine to solve the symmetric eigenvalue problem by parallel Jacobi method on the ICL Distributed Array Processor (DAP), in DAP library (1986).

with M. Marletta. Package of codes SL01F–SL09F for solution of Sturm–Liouville problems and ancillary calculations. Available on NAg Library website (1990/91) and in NETLIB.

with B.R. Stephens. The DAPRE package, a general purpose tool for Automatic Differentiation of Fortran code (1990/91) written jointly with NAg Ltd. Available in NETLIB.

with W. Govaerts. BEMW, a reverse communication Fortran code for the stable solution of linear systems with wider borders (1993). Available in NETLIB.

with J.K. Reid & D. Cowey. AD01: a Fortran 90 package for automatic differentiation, Harwell Subroutine Library January 1996. Replaced by AD02 (2002).

SLDRIVER, a tool for exploring Sturm–Liouville problems and solvers. With SLTSTPAK, a testing package interface for Sturm–Liouville solvers. (See ACM Trans. Math. Software 1999, above). Available in ACM Collected Algorithms at http://www.acm.org/calgo.

### Research

**Collaboration**

I continue to work with Prof Ned Nedialkov at McMaster University on developing methods for numerical solution of differential algebraic equations by Taylor series, and improving our code DAETS. Also on using the structural analysis that underlies our approach as a tool for the better understanding of equation-based models in science and engineering, especially those that are built by interactive modeling tools such as Simulink and Maplesim.

**External Funding.**

PhD project funded by Leverhulme Trust “Improving Structural Analysis for Differential-Algebraic Equation Systems”. Start date autumn 2011.

**Standardisation Work**

Senior Technical Editor, IEEE Working Group P1788 “A Standard for Interval Arithmetic”.

### Biography

BA – Mathematics, Cambridge, 1962.

PhD – Pure Mathematics, Newcastle upon Tyne, 1965.

Cert Ed – Bristol, 1966.

**Previous Positions**

Teacher, Abingdon School, 1966-68.

Lecturer, Aberdeen University 1968–75.

Lecturer, Bristol University 1975–88.

Sabbatical year, University of Toronto, 1982–83.

Lecturer/Senior Lecturer, Cranfield University Shrivenham campus, 1988 – 2006. (Royal Military College of Science, now Defence College of Management and Technology).

Tutor, Open University, 1998 – 2002.

**Interests**

Hill-walking, woodwork, poetry, classical and jazz music.