Numerical Publications

Books

  1. Numerical Methods in Practice -- A Guide to the NAG Library, Hopkins, T.R. and Phillips, C., Addison-Wesley, Reading, MA, USA, 1988.    <#9>

Journal Articles

  1. Certification of Algorithm 734: A Fortran 90 Code for Unconstrained Nonlinear Minimization, Hopkins, T.R., ACM Trans. Math. Software, 24(3), pages 351-354, Sep 1998. [Abstract, Paper]    <#39>
  2. Restructuring the BLAS Level-1 Routine for Computing the Modified Givens Transformation, Hopkins, T.R., ACM SIGNUM, 32(4), pages 2-14, Oct 1997. [Abstract, Paper]    <#38>
  3. Transputer Data-flow Solution for Systems of Linear Equations, Hopkins, T.R. and Welch, P.H., Concurrency: Practice and Experience, 8(8), pages 569-580, 1996.    <#33>
  4. A Parallel Implementation of the Restarted GMRES Iterative Method for Nonsymmetric Systems of Linear Equations, da Cunha, R.D. and Hopkins, T.R., Advances in Computational Mathematics, 2(3), pages 261-277, 1994. [Abstract, Paper]    <#30>
  5. Parallel Preconditioned Conjugate-Gradient Methods, da Cunha, R.D. and Hopkins, T.R., Transputer Communications, 1(2), pages 111-125, Nov 1993. [Abstract, Paper]    <#27>
  6. A Comment on the Eispack Machine Epsilon Routine, Hopkins, T.R. and Slater, J.B., ACM SIGNUM, 28(4), pages 2-6, Oct 1993. [Abstract, Paper]    <#28>
  7. Remark on Algorithm 540, Hopkins, T.R., ACM Trans. Math. Software, 18(3), pages 343-344, Sep 1992.    <#26>
  8. ASR49 -- A Remark on Algorithm AS135: Min-Max Estimates for Linear Multiple Regression Problems, Grant, P.M. and Hopkins, T.R., J. Roy. Statist. Soc. Ser. C, 32, pages 345-347, 1983.    <#7>
  9. Peripheral and ADI Hopscotch Methods for Two Dimensional Parabolic and Elliptic Equations with a Mixed Term, Broom, M.A. and Hopkins, T.R., J. Comput. Appl. Math., 9, pages 239-246, 1983.    <#6>
  10. AS193 -- A Revised Algorithm for the Spectral Test, Hopkins, T.R., J. Roy. Statist. Soc. Ser. C, 32, pages 328-335, 1983.    <#5>
  11. AS188 -- Estimation of the Order of Dependence in Sequences, Hopkins, T.R., Welch, P.H. and Kollerstrom, J., J. Roy. Statist. Soc. Ser. C, 32, pages 185-196, 1983.    <#3>
  12. On the Sensitivity of the Coefficients of Pade Approximants with Respect to their Defining Power Series Coefficients, Hopkins, T. R., J. Comput. Appl. Math., 8, pages 105-109, 1982.    <#47>
  13. Corrections to Fortran Subroutines for the Solution of Toeplitz Sets of Linear Equations, Hopkins, T.R., IEEE Trans. Acoust. Speech Signal Process., 29, pages 1212, 1981.    <#46>
  14. Kufarev's Method for Determining the Schwarz-Christoffel Parameters, Hopkins, T.R. and Roberts, D.E., Numer. Math., 33, pages 353-365, 1979.    <#35>
  15. Some Quadrature Rules for Galerkin Methods Using B-spline Basis Functions, Hopkins, T.R. and Wait, R., Comput. Methods Appl. Mech. Engrg., 19, pages 401-416, 1979.    <#24>
  16. Note on a Family of Economical Sixth Order Finite Difference Methods for Non-linear 2-Point Boundary Value Problems, Hopkins, T.R., BIT, 18, pages 497-499, 1978.    <#2>
  17. A Comparison of Galerkin, Collocation and the Method of Lines for Partial Differential Equations, Hopkins, T.R. and Wait, R., Internat. J. Numer. Methods Engrg., 12, pages 1081-1107, 1978.    <#13>
  18. A Comparison of Numerical Methods for the Solution of Quasilinear Partial Differential Equations, Hopkins, T.R. and Wait, R., Comput. Methods Appl. Mech. Engrg., 9, pages 181-190, 1976.    <#1>

Conference Articles

  1. A Comparison of Acceleration Techniques Applied to the SOR Method, da Cunha, R.D. and Hopkins, T.R., In A. Cuyt, editor, Proceedings on Nonlinear Numerical Methods and Rational Approximation, pages 247-260, Dordrecht, The Netherlands, Mar 1994. Kluwer Academic Publishers Group. [Abstract, Paper]    <#31>
  2. Porting Linear Algebra Subroutines from Transputers to Clusters of Workstations, da Cunha, R.D. and Hopkins, T.R., In R. Grebe, J. Hektor, S.C. Hilton, M.R. Jane and P.H. Welch, editors, Proceedings of the World Transputer Congress, pages 660-667, Amsterdam, 1993. IOS. [Abstract, Paper]    <#29>
  3. The Parallel Solution of Triangular Systems of Linear Equations, R. D. da Cunha and T. R. Hopkins, In M. Durand and F. El Dabaghi, editors, High Performance Computing II, pages 245-255, Amsterdam, New York, Oxford, 1991. North Holland-Elsevier Science Publishers. [Abstract, Paper]    <#49>
  4. A Comparative Study of some Iterative Methods to Solve Systems of Linear Equations using Transputer Nets, da Cunha, R.D. and Hopkins, T.R., In J. Edwards, editor, Occam and the Transputer -- Current Developments, pages 85-99, Amsterdam, 1991. IOS.    <#21>
  5. Parallel Overrelaxation Algorithms for Systems of Linear Equations, da Cunha, R.D. and Hopkins, T.R., In P. Welch, D. Stiles, T.L. Kunii and A. Bakkers, editors, Transputing '91, pages 159-169, Amsterdam, 1991. IOS. [Abstract, Paper]    <#20>
  6. Distributing Matrix Eigenvalue Calculations Over Transputer Arrays, Hopkins, T.R. and Vowden, B.J., In H.S.M. Zedan, editor, Real-time Systems with Transputers, pages 305-312, Amsterdam, 1990. IOS. [Abstract, Paper]    <#18>
  7. A Generally Configurable Multigrid Implementation for the Solution of Three-Dimensional Elliptic Equations on a Transputer Network, El-Giar, O. and Hopkins, T.R., In Kunii, T.L. and May, D., editors, Transputer/occam Japan 3, pages 35-45, Amsterdam, 1990. IOS. [Abstract, Paper]    <#16>
  8. The Parallel Solution of Linear Elliptic Equations using Hopscotch Algorithms, El-Giar, O. and Hopkins, T.R., In Freeman, L. and Phillips, C., editors, Applications of Transputers 1 -- Proceedings of the First International Conference on Applications of Transputers, Liverpool, pages 151-159, Amsterdam, 1990. IOS. [Abstract, Paper]    <#14>
  9. A Generally Configurable Multigrid Implementation for Transputer Networks, El-Giar, O. and Hopkins, T.R., In J. Wexler, editor, Developing Transputer Applications, pages 80-88, Amsterdam, 1989. IOS. [Abstract, Paper]    <#15>
  10. Transputer Data-flow Solutions for Systems of Linear Equations, Hopkins, T.R. and Welch, P.H., In Joubert, G.R., Evans, D.J. and Peters, F.J., editors, Parallel Computing '89 -- Proceedings of the International Conference, Leiden, pages 195-200, Amsterdam, New York, Oxford, 1989. North Holland-Elsevier Science Publishers.    <#12>
  11. Portable Numerical Software for Microprocessors, Genz, A.C. and Hopkins, T.R., In Hennell, M.A. and Delves, L.M., editors, Production and Assessment of Numerical Software, New York, 1980. Academic Press.    <#43>

Collection Articles

  1. The Parallel Solution of Systems of Linear Equations using Iterative Methods on Transputer Networks, da Cunha, R.D. and Hopkins, T.R., In J. Luo and G.L. Reijns, editors, Transputing for Numerical and Neural Network Applications, pages 1-13. IOS, Amsterdam, 1992. [Abstract, Paper]    <#25>
  2. The Parallel Solution of Partial Differential Equations on Transputer Networks, da Cunha, R.D. and Hopkins, T.R., In J. Luo and G.L. Reijns, editors, Transputing for Numerical and Neural Network Applications, pages 96-109. IOS, Amsterdam, 1992. [Abstract, Paper]    <#23>

Working Papers

  1. PIM 2.0: The Parallel Iterative Methods Package for Systems of Linear Equations. User's Guide (Fortran 77 version), R. D. da Cunha and Tim Hopkins, Report 1-96, Computing Laboratory, University of Kent at Canterbury, Canterbury, Kent CT2 7NF, U.K., Jan 1996. [Abstract, Paper]    <#53>
  2. Remark on Applied Statistics Algorithm AS030 Half-Normal Plotting, Tim Hopkins and David Morse, Report 28-94, Computing Laboratory, University of Kent at Canterbury, Canterbury, Kent CT2 7NF, U.K., Dec 1994. [Paper]    <#51>
  3. Remark on Applied Statistics Algorithm AS057 Printing Multidimensional Tables, Tim Hopkins and David Morse, Report 29-94, Computing Laboratory, University of Kent at Canterbury, Canterbury, Kent CT2 7NF, U.K., Dec 1994. [Paper]    <#50>
  4. The Parallel Iterative Methods (PIM) Package for the Solution of Systems of Linear Equations on Parallel Computers, Tim Hopkins and Rudnei Dias da Cunha, Report 19-94, Computing Laboratory, University of Kent at Canterbury, Canterbury, Kent CT2 7NF, U.K., Sep 1994. [Abstract, Paper]    <#52>
  5. Using Parallel Programming Environments on Clusters of Workstations, R. D. da Cunha and Tim Hopkins, Report 12-93, Computing Laboratory, University of Kent at Canterbury, Canterbury, Kent CT2 7NF, U.K., Dec 1993. [Abstract, Paper]    <#54>
  6. NAG Spline Fitting Routines on a Graphics Workstation -- the Story So Far, Tim Hopkins, Report 76, Computing Laboratory, University of Kent at Canterbury, Canterbury, Kent CT2 7NF, U.K., Jul 1990. [Paper]    <#55>

Supervised Theses

  1. A Study on Iterative Methods for the Solution of Systems of Linear Equations on Transputer Networks, R.D. da Cunha, PhD thesis, University of Kent Canterbury, UK, Jul 1992.    <#57>
  2. Implementation and Comparison of Numerical Algorithms for the Solution of Linear Systems using Transputer Networks, J.D. dos Santos, PhD thesis, University of Kent Canterbury, UK, Sep 1990.    <#56>
  3. The Parallel Solution of Elliptic Equations on Transputer Networks, M.O. El-Giar, PhD thesis, University of Kent Canterbury, UK, Mar 1990.    <#58>