Publications

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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, apr, Volume 2, Number 3, Basel, p.261–277, (1994) Abstract

Also as TR-7-93, Computing Laboratory, University of Kent at Canterbury

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The Parallel Solution of Partial Differential Equations on Transputer Networks, da Cunha, R.  D., and Hopkins T.  R. , Amsterdam, p.96–109, (1992) Abstract

Also as TR-17-92, Computing Laboratory, University of Kent at Canterbury, U.K.

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New Parallel (Rank-Revealing) {QR} Factorization Algorithms, da Cunha, R.  D., Becker D., and Patterson J.  C. , Euro-Par 2002, Number 2400, Berlin, p.677–686, (2002) Abstract

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A multiresolution algorithm to generate images of generalized fuzzy fractal attractors, da Cunha, R.  D., Oliveira E.  R., and Strobin F. , Numerical Algorithms, (2020) AbstractWebsite

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PIM 2.0 – the Parallel Iterative Methods Package for Systems of Linear Equations User's Guide – Fortran 77 Version, da Cunha, R.  D., and Hopkins T.  R. , jun, (1995) Abstract

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PIM 2.0 – the Parallel Iterative Methods Package for Systems of Linear Equations User's Guide (Fortran 77 Version), da Cunha, R.  D. , (1995) Abstract

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Parallel Preconditioned {Conjugate-Gradients} Methods on Transputer Networks, da Cunha, R.  D., and Hopkins T.  R. , Transputer Communications, Volume 1, Number 2, p.111–125, (1993) Abstract

Also as TR-5-93, Computing Laboratory, University of Kent at Canterbury, U.K.

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A Study on the Parallel, Iterative Solution of Systems of Linear Equations appearing on Analytical Nodal Schemes for Two-Dimensional Cartesian Geometry Discrete Ordinates Problems, da Cunha, R.  D., Tres A., and Barichello L.  B. , ANS MC2015 - Joint International Conference on Mathematics and Computation (M&C), Supercomputing in Nuclear Applications (SNA) and the Monte Carlo (MC) Method, p.1–12, (2015) Abstract

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A multiresolution algorithm to approximate the Hutchinson measure for IFS and GIFS, da Cunha, R.  D., Oliveira E.  R., and Strobin F. , Communications in Nonlinear Science and Numerical Simulation, (2020) AbstractWebsite

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A Parallel Implementation of the Restarted GMRES Iterative Method for Nonsymmetric Systems of Linear Equations, da Cunha, R.  D., and Hopkins T.  R. , apr, (1993) Abstract

Also in: {\em Advances in Computational Mathematics}, 2(3):261-277, J.C. Baltzer, April 1994

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Using Parallel Programming Environments on Clusters of Workstations, da Cunha, R.  D., and Hopkins T.  R. , nov, (1993) Abstract

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The Parallel Iterative Methods (PIM) Package for the Solution of Systems of Linear Equations on Parallel Computers, da Cunha, R.  D., and Hopkins T.  R. , Applied Numerical Mathematics, Volume 19, Number 1-2, p.33–50, (1995) Abstract

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A benchmark study based on the Parallel computation of the vector outer-product $A = uv^{T}$ operation, da Cunha, R.  D. , Concurrency: Practice & Experience, Volume 9, Number 8, New York, p.803–819, (1997) Abstract

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The Parallel Solution of Systems of Linear Equations Using Iterative Methods on Transputer Networks, da Cunha, R.  D., and Hopkins T.  R. , Amsterdam, p.1–13, (1992) Abstract

Also as TR-16-92, Computing Laboratory, University of Kent at Canterbury, U.K.

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Dynamic block GMRES: an iterative method for block linear systems, da Cunha, R. D., and Becker D. , 2007, Volume 27, Issue 4, p.423 - 448, (2007) AbstractWebsite

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We present variants of the block-GMRES($m$) algorithms due to Vital and the block-LGMRES($m$,$k$) by Baker, Dennis and Jessup, obtained with replacing the standard QR factorization by a rank-revealing QR factorization in the Arnoldi process. The resulting algorithm allows for dynamic block deflation whenever there is a linear dependency between the Krylov vectors or the convergence of a right-hand-side occurs. $\textsc{Fortran 90}$implementations of the algorithms were tested on a number of test matrices and the results show that in some cases a substantial reduction of the execution time is obtained. Also a parallel implementation of our variant of the block-GMRES($m$) algorithm, using $\textsc{Fortran 90}$and $\textsc{MPI}$was tested on $\textsc{SunFire 15K}$parallel computer, showing good parallel efficiency.

Porting Linear Algebra Subroutines From Transputers To Clusters of Workstations, da Cunha, R.  D., and Hopkins T.  R. , apr, (1993) Abstract

Also in: Proceedings of the ``World Transputer Congress'' conference, September 20–22, 1993, Aachen, V.1, pp. 660-667

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PIM 1.1} – the Parallel Iterative Methods Package for Systems of Linear Equations {User's Guide – Fortran 77 Version, da Cunha, R.  D., and Hopkins T.  R. , jan, (1994) Abstract

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The Parallel Iterative Methods (PIM) Package for the Solution of Systems of Linear Equations on Parallel Computers, da Cunha, R.  D. , (1995) Abstract

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