### Project Description

RESEARCH AREAS:

Scientific Computing

Symbolic Computing

Reliability of Numerical Methods for Dynamical Systems

CONTACT:

Western University

Middlesex College 272

London, Ontario, Canada N6A 5B7(519) 661-2111 x88785

# ROBERT CORLESS

**Professor; **

Department of Applied Mathematics, Philosophy, and Computer Science, Western University

Robert M. Corless is a full professor (Since 1998) in the department of Applied Mathematics at Western, first appointed in 1987. He was born in Prince George, British Columbia. His background is mechanical engineering, numerical analysis, and computer algebra. He was the Editor of the Bulletin of the Special Interest Group on Symbolic and Algebraic Manipulation (SIGSAM) (Communications in Computer Algebra, a publication of the Association for Computing Machinery, and was later Chair of SIGSAM. He was the Chair of the Department of Applied Mathematics from 2002 till 2007. Though an active researcher and speaker, he is also intensely interested in teaching, especially in the influence and utility of technology in teaching, when properly used. He holds honorary appointments in both the Department of Computer Science and in the Department of Philosophy.

One of the founders of a field of computational mathematics known as numerical nonlinear algebra, Robert Corless’s multi-disciplinary background has enabled him to make contributions to many areas, including flow-induced vibration, non-linear dynamics and computer algebra. His most highly-cited works are those on the Lambert W function, co-authored with D.E. Knuth, David Jeffrey and others.

**Books:**

R.M. Corless and N. Fillion, **A Graduate Survey of Numerical Methods**, in preparation 2011, 650 pages.

R.M. Corless, **Essential Maple 7** Springer-Verlag, March 2002, 282 pages.

R.M. Corless, C. Essex and P.J. Sullivan, **First Year Engineering Mathematics Using Supercalculators, **SciTex, The University of Western Ontario 1991, 1992, 1993 (2nd ed), 1995, 400 pages.

**Refereed Journal Articles:**

P. W. Lawrence, R.M. Corless, and D.J. Jeffrey, “Complex Double-Precision Evaluation of the Wright $omega$ Function”, accepted August 2010 for ACM Transactions on Mathematical Software.

J.C. Butcher, R.M. Corless, L. Gonzalez-Vega and A. Shakoori, “Polynomial Algebra for Birkhoff Interpolants”, Numerical Algorithms Vol 56 No 3 (2011), pp. 319–347.

P. Yu and R. M. Corless, “Symbolic computation of limit cycles associated with Hilbert’s 16th problem”, Comm. Nonlinear Science and Numerical Simulation, Vol 14, (2009), pp. 4041–4056.

R. M. Corless, K. Gatermann, & I.S. Kotsireas, “Using symmetries in the eigenvalue method for polynomial systems”, Special Issue of the Journal of Symbolic Computation (Chemistry and Biological Applications) in honour of Karin Gatermann 44:11 1536-1550.

S. Brennan & R. M. Corless, “Creating a Warmer Environment for Women in the Mathematical Sciences and in Philosophy”, Atlantis, Vol 33(2) 2009 pp 54–61.

A. Amiraslani, P. Lancaster & R. M. Corless, “Linearization of matrix polynomials expressed in polynomial bases”, IMA Journal of Numerical Analysis Vol 29, No. 1, pp 141–157 (2009).

M. Bronstein, R. M. Corless, J.H. Davenport & D.J. Jeffrey, “Algebraic Properties of the Lambert *W* Function from a result of Rosenlicht and of Liouville”, Integral Transforms and Special Functions, Vol. 19(10) (2008) pp. 709-712.

R.M.Corless, A. Shakoori, D.A. Aruliah, & L. Gonzalez-Vega, “ Barycentric Hermite Interpolants for Event Location in Initial-Value Problems” Journal of Numerical Analysis, Industrial and Applied Mathematics, Vol. 3, no. 1-2 (2008) pp. 1-16.

R.M. Corless & S. Ilie, “Polynomial cost for solving IVP for high-index DAE” BIT Numerical Mathematics, (2008) 48: 29-49.

G. Söderlind, S. Ilie & R. Corless, “Adaptivity and Computational Complexity in the Numerical Solution of ODEs”, Journal of Complexity, 24 3 (2008) 341-361.

S. Ilie, R. M. Corless & G.C. Essex, “The computational complexity of extrapolation methods”, Mathematics in Computer Science DOI 10.1007/s11786-007-0040-4 2008.

A. Amiraslani, D.A. Aruliah and R.M. Corless, “Block *LU *Factors of Generalized Companion Matrix Pencils”, Theoretical Computer Science 381.1-3 (2007) 134-147.

R. M. Corless, N. Rezvani, & A. Amiraslani, “Pseudospectra of matrix polynomials expressed in alternative bases”, Mathematics and Computer Science, 1 (2007) 353-374.

C. Essex, S. Ilie, and R. Corless, “Symmetry Breaking and Long-Term Forecasting”, J. Geophys. Research (2007) Vol. 112, D24S17, 9 pgs.

J. Zhao, M. Davison & R. Corless (2007). “Compact Finite Difference Method for American Option Pricing”. Journal of Computational and Applied Mathematics 26(1), 306-321.

R.M. Corless, “On a generalized companion matrix pencil for matrix polynomials expressed in the Lagrange basis”, Trends in Mathematics (2007) 1-16.

J. Zhao, R. Corless & M. Davison “Financial Applications of Symbolically Generated Compact Finite Difference Formulae” Trends in Mathematics (2006) 361-374.

S. Ilie, R. M. Corless & G. J. Reid, “Numerical solutions of index-1 differential algebraic equations can be computed in polynomial time”, Numer. Algorithms 41, (2006) 161-171.

Jichao Zhao & R.M. Corless, “Compact Finite Difference Method for Integro-Differential Equations”, Appl. Math. Comput. 177, No. 1, (2006) 271-288.

J. Zhao, T. Zhang, & R.M. Corless, “Convergence of compact finite difference methods for second-order elliptic equations”, Appl. Math. Comput. 182, No. 2, (2006) 1454-1469.

J. M. Heffernan & R.M. Corless, “Solving some delay differential equations with computer algebra”, The Mathematical Scientist, 31, no. 1, (2006) 21-34.

M. Benghorbal & R.M. Corless, “A unified formula for arbitrary order symbolic derivatives and integrals of a rational polynomial”, Int. J. Pure & Appl, Math, 16, no. 2 (2004) 193-201.

M. Benghorbal & R.M. Corless, “Power series solutions of fractional differential equations”, Int. Journal of Pure and Applied Mathematics, 15, no. 3 (2004) 333-352.

R.M. Corless, S.M. Watt & L. Zhi, “QR Factoring to compute the GCD of univariate approximate polynomials”, IEEE Trans. Sig. Proc., 52, no. 12, December 2004, 3394-3402.

R.J. Bradford, R.M.Corless, J.H.Davenport, D.J.Jeffrey, & S.M. Watt: “Reasoning about the elementary functions of complex analysis”, Ann. Maths Art. Intel., 36, 2002, 303-318

R.M. Corless, “A new view of the computational complexity of initial value problems for ordinary differential equations”, Numerical Algorithms, 31 (2002) 115-124.

S.R. Valluri, R.M. Corless, & D.J. Jeffrey, “Some applications of the Lambert W function to physics”, 78, Canadian J. of Physics (2000) 823-831.

Lawrence F. Shampine & R.M. Corless, “Initial value problems for ODEs in problem solving environments”, J. Computational and Applied Mathematics, 125 (2000) 31-40.

E. Kaltofen, with R.M. Corless & D.J. Jeffrey, “Challenges in symbolic computation: My favourite open problems”, 29, 6 Journal of Symbolic Computation, July (2000) 891-919.

J.M. Borwein & R.M. Corless, “Emerging tools in experimental mathematics”, American Mathematical Monthly, vol. 106, December 1999, 889-909.

E. Katende, A. Jutan & R.M. Corless, “Quadratic non-linear predictive control”, Industrial and Engineering Chemistry Research, 37 (1998), 2721-2728.

R.M. Corless, “Variations on a theme of Newton”, vol. 71, Math Mag, Feb 1998, 34-41.

D. J. Jeffrey, D.E.G. Hare, & R.M. Corless, “Exact rational solutions of a transcendental equation”, Comptes Rendus (Mathematics), vol 20, 3 (1998) 71-76.

Heinz Bauschke & R.M. Corless, “Analyzing a projection method with Maple”, Maple Tech (special issue Maple in the Mathematical Sciences), vol 4, no. 1 (1997) 2-7.

R.M. Corless & D.J. Jeffrey, “Scientific computing: One part of the revolution”, special issue J. of Symbolic Computation 23 (1997) 485-495.

R.M. Corless, D.J. Jeffrey, Pratibha & M.B. Monagan, “Two perturbation calculations in fluid mechanics using large expression management” J. Symbolic Computation, 23 (1997) 427-443.

J.M. Borwein, P.B. Borwein, S. Braham, R. Corless, & L. Jorgenson, “Digitally activated mathematics for a brave new world wide web”, Ed. Res. & Perspec, 23, no. 2 (1996) 28 47.

R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey & D.E. Knuth, “On the Lambert *W* function”, Advances in Computational Mathematics 5 (1996) 329-359.

D.J. Jeffrey, D.E.G. Hare & R.M. Corless, “Unwinding the branches of the Lambert W Function”, Mathematical Scientist, 21, (1996) 1-7.

R.M. Corless, “Simple engineering mathematics with Maple”, Special Issue of MapleTech on Engineering, Ross Taylor ed., vol 3, no. 1 (1996) 2-7.

R.M. Corless, “Symbolic computation in nonlinear dynamics” Open Systems and Information Dynamics vol. 3 (1) (1995) 131-148.

D.J. Jeffrey, R.M. Corless, D.E.G. Hare & D.E. Knuth, “Sur l’inversion de *ya*ey au moyen des nombres de Stirling associés, Comptes Rendus de L’Académie des Sciences, Paris, 320, 1, 12 (1995) 1449-1452.

R.M. Corless, “Bifurcation in a flow-induced vibration model”, American Math Society; Fields Institute Communications, vol. 4 (1995) 43-59.

R.M. Corless & S. Yu Pilyugin, “Approximate and real trajectories for generic dynamical systems”, J. Mathematical Analysis & Applications, 189 (1995) 409-423.

R.M. Corless & S. Yu Pilyugin, “Evaluation of upper Lyapunov exponents on hyperbolic sets”, Journal of Mathematical Analysis and Applications 189 (1995) 145-159.

R.M. Corless, “What good are numerical solutions of chaotic differential equations?”, Computers in Mathematics with Applications vol 28, no. 10-12 (1994) 107-121.

T. Scott, G. Fee. R. Corless & M. Monagan, “Applications of Maple to mathematical, scientific, and engineering problems”, Special Issue of MapleTech (1994) 49-57.

T. Scott, B. Madore & R.M. Corless, “Maple in Science education” Special Issue of MapleTech (1994) 58-68.

R.M. Corless, “Error backward”, Contemporary Mathematics 172 (1994) 31-62.

R.M. Corless, G.H. Gonnet, D.E.G. Hare and D.J. Jeffrey, “Lambert’s W function in Maple”, MapleTech #9 (1993) 12-22.

A.G. Connell & R.M. Corless, “An Experimental interval arithmetic package in Maple”, Interval Computations, No. 2, (1993) 120-134.

R.M. Corless, “Six, Lies, and Calculators” The American Mathematical Monthly, vol 100, no 4, (1993) 344-350.

**Book Chapters:**

D.J. Jeffrey, R.M. Corless, “Linear Algebra in Maple, ** CRC Handbook of Linear Algebra**” Leslie Hogben ed. (2007) pp 72.1-72.21.

R.M. Corless, E. Kaltofen. S.M. Watt, “Hybrid Methods”, in Computer Algebra Handbook, Springer, eds. J. Grabmeier, E. Kaltofen, V. Weispfenning, December 2002, 113-125.

R.M. Corless, “First Encounters of an AXIOM-XL Novice”, in the AXIOM-XL Library Compiler User Guide, NAG, 1994, 293-320.

R.M. Corless & G.V. Parkinson, “Mathematical modelling of the combined effects of vortex-induced vibration and galloping, Part II”, J. of Fluids & Structures 7, (1993) 825-848.

T.C. Scott, M.B. Monagan, G.J. Fee & R.M. Corless, “Applications of Maple to mathematical, scientific and engineering problems”, Special issue Maple Tech, (1994) 49-57

P.A. Rosati, R.M. Corless, C. Essex, & P. Sullivan, “An evaluation of the HP28S calculator in calculus” Australian J. of Engineering Education vol 3, no. 1 (1992) 79-88.

R.M. Corless, “Defect-controlled numerical methods and shadowing for chaotic differential equations”, Physica D 60 (1992) 323-334. (special issue on Experimental Mathematics: Computational Issues in Nonlinear Science)

R.M. Corless, “Continued fractions and chaos”, The American Mathematical Monthly vol. 99, no. 3, March (1992) 203-215.

R.M. Corless, D.J. Jeffrey & H. Rasmussen, “Numerical evaluation of Airy functions with complex arguments”, J. Computational Physics vol. 99, no. 1 March (1992) 106-114.

R.M. Corless, C. Essex, M.A.H. Nerenberg, “Numerical methods can suppress chaos”. Physics Letters A 157, 1 (1991) 27-36.

R.M. Corless, G.W. Frank & J.G. Monroe, “Chaos & Continued Fractions”, Physica D. 46 (1990) 241-253.

R.M. Corless & D.J. Jeffrey, “Solution of a hydrodynamic lubrication problem with Maple” J. Symbolic Computation 9 (1990) 503-513.

R.M. Corless & G.V. Parkinson, “A model of the combined effects of vortex-induced oscillation and galloping”, J. Fluids and Structures 2 (1988) 203-220.

R.M. Corless & D.J. Jeffrey, “Stress moments of nearly touching spheres in low Reynolds number flows”, ZAMP 39 (1988) 874-884.

D.J. Jeffrey & R.M. Corless, “Forces and Stresslets for the axisymmetric motion of nearly touching unequal spheres”, J. Phisico-Chemical Hydrodynamics, vol. 10, no. 4 (1988) 461-470.

**Invited Talks:**

“Pseudospectra of Matrix Exponential Polynomials”, SNC 2009, August, Kyoto, Japan

“Polynomial Algebra by Values” Special Semester on Gröbner Basis, ApCoA, Linz, Austria, February 19-25, 2006.

“On a Generalized Companion Matrix Pencil for Matrix Polynomials Expressed in the Lagrange Basis”, International Workshop on Symbolic-Numeric Computation, Xi’an, China, July19-21, 2005.

“Numerical Nonlinear Algebra” COSCOMP Conference on Scientific Computing, Vienna, Austria, June 9-11, 2005.

“Computer-Mediated Thinking”, Invited plenary lecture at “Technology in Mathematics Education”, TIME 2004, Montreal, July 2004.

**Refereed Conference Proceedings:**

R. M. Corless, H. Ding, N.J. Higham, & D.J.Jeffrey, “The solution of *S *exp *S *= *A *is not always Lambert W(*A*)”, Proc. ISSAC 2007.

R. M. Corless & D. Assefa, “A Case Study on Elliptic Functions in a CAS: Jeffery- Hamel Flow in Maple”, Proc. ISSAC 2007.

R.M. Corless, Y. Lin, L. Ma & J. Zhao, “A highly efficient and accurate algorithm for solving partial differential equation in cardiac tissue models” WSEAS 2006, Miami, USA, Jan 18-20, 2006.

W. Zou, D.J. Jeffrey & R.M. Corless, “Fraction-free forms of LU matrix factoring”, Proceedings of Transgressive Computing 2006, Granada, Spain, (2006) 443-446.

R.M. Corless, S. Ilie, & G. Reid, “Computational complexity of numerical solution of polynomial systems”, Proc. Transgressive Comput 2006, Granada, Spain (2006) 405-408.

R.M. Corless, “On a Generalized Companion Matrix Pencil for Matrix Polynomials Expressed in the Lagrange Basis”, SNC 2005, Xi’an, China, D. Wang & L. Zhi eds. July 19-21, 2005, 1-18.

J. Zhao, R.M. Corless, M. Davison, “Financial Applications of Symbolically Generated Compact Finite Difference Formulae”, SNC 2005, Xi’an, China, D. Wang & L. Zhi eds. July 19-21, 2005, 220-234.

R.M. Corless & S.M. Watt, “Bernstein Bases are Optimal, but, sometimes, Lagrange bases are Better, Symbolic and Numeric Algorithms for Scientific Computing, SYNASC (2004) 141-152.

D.A. Aruliah, & R.M. Corless, “Numerical Parameterization of Affine Varieties Using ODEs”, Proc ISSAC 2004, University of Cantabria, Santander, Spain, J. Gutierrez, ed. (2004) 12-18.

R.M. Corless, “Generalized Companion Matrices in the Lagrange Basis”, Proc EACA 2004, University of Cantabria, Santander, Spain, L. González Vega, T. Recio, eds. (2004) 317-322.

R.M. Corless, L. Gonzalez-Vega, I. Necula, A. Shakoori, “Topology Determination of Implicitly Defined Real Algebraic Plane Curves”, An. Univ. Timisoara Ser. mat.-Inform., 41 (Special Issue): (2003) 83-96.

R.M. Corless, Andre Galligo, I.S. Kotsireas, S.M. Watt, “A Geometric-Numeric Algorithm for Absolute Factorization of Multivariate Polynomials”, Proc ISSAC (2002) 37-45.

R.M. Corless & D.J. Jeffrey, “On the Wright w* *Function”, Proceedings of Joint International Conferences, AISC Artificial Intelligence, Automated Reasoning 2002, and Symbolic Computation, and Calculemus 2002, Marseille, France, July 2002, 76-90.

R.M. Corless, M.W. Giesbrecht, M. van Hoeij, I.S. Kotsireas, & S.M. Watt, “Towards Factoring Bivariate Approximate Polynomials”, Proc ISSAC 2001, UWO, London, Canada, B. Mourrain, ed. (2001) 85-92.

D.J. Jeffrey, M.W. Giesbrecht, & R.M. Corless, “Integer Roots Computation for Integer-power- content Calculations”, Computer Mathematics, Proc ASCM 2000,World Scientific Lecture Notes Series on Computing, vol. 8, (2001) 71-74.

R.M. Corless, M.W. Giesbrecht, I. Kotsireas, & S.M. Watt, “Numerical Implicitization of Curves and Surfaces”, Proc AISC, Madrid, LNAI vol. 1930, (2001) 174-183.

R.M. Corless, J.H. Davenport, D.J. Jeffrey, G. Litt, & S.M. Watt, “Reasoning About the Elementary Functions of Complex Analysis”, Proc AISC (2001) 115-126.

R.M. Corless, “Symbolic-Numeric Algorithms for Polynomials: some recent results”, Proceedings of Dagstuhl Seminar, Symbolic-Algebraic and Verification Methods, Dagstuhl, Germany (2001), 21-22.

R.M. Corless, M. W. Giesbrecht, D.J. Jeffrey, & S.M. Watt, “Approximate Polynomial Decomposition”, Proceedings ISSAC ’99, Vancouver, ed. S. Dooley, (1999) 213-220.

Paulina Chin, R. M. Corless, and George F. Corliss, “Optimization Strategies for the Approximate GCD Problem”, Proc. ISSAC 1998, 228-235.

J.M. Borwein, P.B. Borwein, R.M. Corless, Loki Jörgenson, “What is Organic Mathematics”, Proc. Organic Mathematics Workshop, Dec. 12-14, 1995. eds.

J.M.Borwein, P.B. Borwein, R.M. Corless, & L. Jorgenson; http://www.cecm.sfu.ca/organics, Canadian Mathematical Society Proceedings vol. 20. (1997), 1-18.

R.M. Corless, “Continued Fractions and Chaos”, Organic Math Workshop Proceedings, vol. 20, (1997) 205-237. (Reprinted from the American Mathematical Monthly with appendices and new material added).

R.M. Corless, P.M. Gianni, & B.M. Trager, “A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots”, Proc. ISSAC, ed. W. Kuechlin, Maui, July 21-23 (1997), 133-140.

R.M. Corless, D.J. Jeffrey, & D.E. Knuth, “A sequence of series for the Lambert W function”, Proceedings ISSAC, ed.W. Kuechlin, Maui, July 21-23, (1997) 197-204.

R.M. Corless & Jacek Rokicki, “The symbolic generation of finite difference formulae”, Proceedings ICIAM ’96, Hamburg, eds. G. Alefeld, O. Mahrenholtz, R. Mennicken, Zeitschrift für Angewandte Mathematik und Mechanik, 76,supp. 1 (1996) 381-382.

Anne-Marie E. Allison and R.M. Corless, “A Bifurcation Study of a flow-induced vibration model”, Proceedings American Soc. Mech. Engineering Meeting on Flow-Induced Vibrations, Montreal, M.J. Pettigrew ed., vol. PVP-328, July 1996, 143-156.

R.M. Corless, “Bifurcation in a flow-induced vibration model”, Proceedings of the Fields Institute Workshop on Normal Forms and Homoclinic Chaos, 1992, eds. W.F. Langford & W. Nagata, Fields Institute Communications, vol. 4 (1995) 43.59

R.M. Corless, P.M. Gianni, B.M. Trager, & S.M. Watt, “The Singular Value Decomposition for Polynomial Systems”, Proc. ISAAC, 1995, 195-207.

R.M. Corless, “Sufficiency conditions in the calculus of variations” Proceedings ISSAC (1994) eds. J. von zur Gathen, M. Giesbrecht; Oxford, U.K., July (1994) 197-204.

R.M. Corless and G.V. Parkinson, “Mathematical modelling of the combined effects of vortex-induced vibration and galloping, Part II”, Proceedings 1992 ASME International Symposium on Flow-Induced Vibration and Noise, vol. 6 (1992) 39-62.

R.M. Corless & Honglin Ye “Solving linear integral equations in Maple”, Proceedings ISSAC Symposium July 27-29, 1992, Berkeley, CA. 95-103.

P.M. Corless, C. Essex, T. Lookman, P.A. Rosati, & P.J. Sullivan, “The HP28S/HP48S in first year engineering mathematics” The Fourth Annual Int’l. Conference on Technology in Collegiate Mathematics, Portland, Oregon, November 15-17, 1991.

R.M. Corless & G.F. Corliss, “Rationale for guaranteed ODE defect control” Proc. of SCAN-91 International Symposium, Oldenburg, Germany.

P.A. Rosati, R.M. Corless, C. Essex, P. Sullivan, “Student Reaction to the HP28s Calculator in Calculus” Proceedings of East-West Congress on Engineering Education, Jagiellonian University, Cracow, Poland, (1991) 80-84.

R.M. Corless, “Chaos in a Flow-induced Vibration Model”, ASME International Symposium on Flow Induced Vibrations and Noise, Chicago 1988, vol. 7, eds M.M. Reischman, M.P. Paidoussis, R.J. Hansen, 77-85.