Publications


  1. Arioli M., 1979. Analisi numerica di una disequazione variazionale legata al moto di un fluido attorno ad un ostacolo. Calcolo, 16, pp 71-91.
  2. Arioli M., Laratta A., and Menchi O., 1983. Numerical study of some feasible direction methods in mathematical programming. J. Optim. Theory Appl., 40, pp 1-23.
  3. Arioli M., Laratta A., and Menchi O., 1984. Numerical computation of the projection of a point onto a polyhedron. J. Optim. Theory Appl., 43, pp 495-525.
  4. Arioli M. and Laratta A., 1984. Metodi diretti per la soluzione di sistemi sottodeterminati. Calcolo, 21, 229-252.
  5. Arioli M. and Laratta A., 1985. Error analysis of an algorithm for solving an underdetermined linear system. Numerische Math., 46, pp 255-268.
  6. Arioli M. and Romani F., 1985. Relations between condition numbers and the convergence of the Jacobi method for real positive definite matrices. Numerische Math., 46, pp 31-42.
  7. Arioli M., Laratta A., and Menchi O., 1985. A big-M method for the computation of projection onto a polyhedron. J. Optim. Theory Appl., 47, pp 17-34.
  8. Arioli M. and Laratta A., 1986. Error analysis of algorithms for computing the projection of a point onto a linear manifold. Linear Alg. and its Applics., 82, pp 1-26.
  9. Arioli M., Demmel J.W., and Duff I. S., 1989. Solving sparse linear systems with sparse backward error. SIAM J. Matrix Anal. and Applics., 10, pp 165-190.
  10. Arioli M., Duff I. S., and deRijk P. P. M., 1989. On the augmented systems approach to sparse least-squares problems. Numerische Math., 55, pp 667-684.
  11. Arioli M., Duff, I. S., Gould, N. I. M., and Reid, J. K., 1990. Use of the P4 and P5 algorithms for in-core factorization of sparse matrices. SIAM J. Sci. Stat. Comput., 11, pp 913-927. 
  12. Arioli M. and Duff I.S., 1990. Experiments in tearing large sparse systems. "Reliable Numerical Computation", editors M. G. Cox, S. Hammarling, Oxford University Press.
  13. Arioli M., Duff I. S., Noailles J., and Ruiz D., 1990. A block iterative method for general sparse equations. Parallel Computing 89, pp 187-193.Download PDF file
  14. Arioli M., Duff I. S., Noailles J., and Ruiz D., 1992. A block projection method for sparse matrices. SIAM J. Sci. Stat. Comput., 13, pp 47-70.
  15. Arioli M. and Romani F., 1992. Stability, convergence and conditioning of stationary iterative methods of the form xi+1 = P xi + q for the solution of linear systems. IMA J. Numer. Anal., 12, pp 21-30.
  16. Arioli M., Duff I. S., and Ruiz D., 1992. Stopping criteria for iterative solvers. SIAM J. Matrix Anal. and Applics., 13, pp 138-144.
  17. Arioli M., Drummond A., Duff I. S., and Ruiz D., 1994. Parallel block iterative solvers for heterogeneous computing environments. "Algorithms and parallel VLSI architectures III, Proceedings of the international workshop" M. Moonen et al. (eds.), Elsevier, 1994. Download PDF file
  18. Arioli M., Duff I. S., Ruiz D., and Sadkane M., 1995. Block Lanczos techniques for accelerating the block Cimmino method. SIAM J. Sci. Comput., 16, pp 1478-1511 .
  19. Arioli M. and Valdettaro L., 1995. Roundoff error analysis of the Fast Cosine Transform and of its application to the Chebyshev pseudospectral method. East-West Journal of Numerical Mathematics, 3, n.1, pp 43--58.
  20. Arioli M., Munthe-Kaas H., and Valdettaro L., 1996. Componentwise error analysis for FFT's with applications to fast Helmholz equations. Numerical Algorithms , 12, pp 65-88.
  21. Arioli M., Codenotti B., and Fassino C., 1996. The Padè Method for computing the matrix exponential. Linear Alg. and its Applics. , 240, pp 111-130.
  22. Arioli M. and Fassino C., 1996. Roundoff error analysis of algorithms based on Krylov subspace methods. BIT, 36, pp 189-206.
  23. Arioli M., Ptak V., and Strakos Z.,1998. Krylov sequences of maximal lenght and convergence of GMRES. BIT, 38, pp 1-9.
  24. Perugia I., Simoncini V., and Arioli M., 1999. Linear Algebra Methods in a Mixed Approximation of Magnetostatic Problems . SIAM J. Sci. Stat. Comput., 21, pp 1085-1101.
  25. Arioli M., 2000. The Use of QR Factorization in Sparse Quadratic Programming and Backward Error Issues.  SIAM J. Matrix Anal. and Applics., 21, pp 825-839. 
  26. Arioli M., Noulard E., and Russo A., 2001. Vector stopping criteria for iterative methods: PDE's applications. CALCOLO, 38 , pp 97-112 .
  27. Arioli M. and Baldini L., 2001. A Backward Error Analysis of a Null Space Algorithm in Sparse Quadratic Programming. SIAM J. Matrix Anal. and Applics., 23 (2), pp 425-442. 
  28. Arioli M. and Manzini G., 2002.A Null Space Algorithm for Mixed Finite Element Approximation of Darcy's Equation. Commun. Numer. Meth. Engng., 18 pp 645--657 . Download Postscript file.
  29. Arioli M. and Manzini G., 2003. Null space algorithm and spanning trees in solving Darcy's equation.  BIT Numerical Mathematics  Download Postscript file.
  30. Arioli M. , 2004. A Stopping Criterion for the Conjugate Gradient Algorithm in a Finite Element Method Framework. Numer. Math.  97, pp 1-24.  The original publication is available at http://www.springerlink.com  Digital Object Identifier (DOI) 10.1007/s00211-003-0500-y. Download PDF file
  31. Arioli M, Loghin D., and Wathen A., 2005, Stopping criteria for iterations in finite-element methods. Numer. Math. 99, pp 381-410.   The original publication is available at http://www.springerlink.com Digital Object Identifier (DOI) DOI: 10.1007/s00211-004-0568-z. Download  file.
  32. Arioli M. and Manzini G., 2005.A Network Programming Approach in Solving Darcy's Equations by Mixed Finite-Element Methods. Electronic Transactions on Numerical Analysis, Special Volume on Saddle Point Problems: Numerical Solution and Applications , 22:17-40. Download PDF file.
  33.  Arioli M. , Maryska J., Rozloznik M., and Tuma M. , 2005. Dual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media. Electronic Transactions on Numerical Analysis, Special Volume on Saddle Point Problems: Numerical Solution and Applications, 22:41-70. Download PDF file.
  34. Arioli M., Baboulin M. , and Gratton S. . 2007. Partial condition number for least-squares problems. SIAM J. Matrix Anal. and Applics., 29 (2):413-433. Download PDF file
  35.  Arioli M., Duff I. S. , Gratton S., and Pralet S., 2007. A note on GMRES preconditioned by a perturbed LDLT decomposition with static pivoting. SIAM J. Sci. Comput. 29 (8):2024-2044.Download PDF file
  36.  Arioli M. and Loghin D., 2009. Stopping criteria for mixed finite element problems.  ETNA, 29:178-193. Download PDF file
  37. Arioli M. and Duff I. S., 2009. Using FGMRES to obtain backward stability in mixed precision. Electronic Transactions on Numerical Analysis, 33:31-44. Download PDF file
  38. Arioli M. and Gratton S., 2008. Least-squares problems, normal equations, and stopping criteria for the conjugate gradient method.  RAL-TR-2008-008. Download PDF file
  39. Arioli M. and Loghin D., 2009. Discrete interpolation norms with applications. RAL-TR-2008-012. To appear on SINUM.  Download PDF file
  40. Arioli M., Kourounis D, and Loghin D., 2008.  Discrete fractional Sobolev norms for domain decomposition preconditioning. RAL-TR-2008-31. Download PDF file
  41. Arioli M and Ruiz D., 2009. Flexible deflation in Krylov methods with Chebyshev-based polynomial filters. RAL-TR-2009-14. Download PDF file
  42. Arioli M., Georgoulis E. H., and Loghin D., 2009. Convergence of inexact adaptive finite element solvers for elliptic problems. RAL-TR-2009-21. DownLoad PDF file
  43. Arioli M., 2010. Generalized Golub-Kahan bidiagonalization and stopping criteria. RAL-TR-2010-008. Download PDf file
  44. Arioli M. and Scott J., 2011.  Chebyshev acceleration of iterative refinement. RAL-TR-2011-010.
    Download PDf file



 
 

Monographs and Software


  1. Arioli M., Laratta A., and Menchi O., 1983. Algoritmi per il calcolo di proiezioni su varietà lineari e su poliedri. Monografie Software Matematico, IAC-CNR, Roma.
  2. Arioli M., Laratta A., and Menchi O., 1984. Algoritmi per la minimizzazione di funzioni convesse su varietà lineari e poliedri. Monografie Software Matematico, IAC-CNR, Roma.
  3. Arioli M., Duff I. S., and Storer N. P., 1988. MC33 - HARWELL Subroutine Library Specification. CSS Division, Harwell Laboratory, England.
  4. Arioli M. and Duff I. S., 1988. MC41 - HARWELL Subroutine Library Specification. CSS Division, Harwell Laboratory, England.
  5. Arioli M. and Duff I. S., 1988. MA40 - HARWELL Subroutine Library Specification. CSS Division, Harwell Laboratory, England.
  6. Arioli M., Chan T. F., Duff I. S., Gould N. I. M., and Reid J. K., 1993. Computing a search direction for large-scale linearly-constrained nonlinear optimizatio calculations. RAL-93-066. Download PDF file.
  7. Noulard E. and Arioli M., 1994. Vector stopping criteria for iterative methods: Theoretical tools. Report IAN # 956, Pavia.
  8. Arioli M. and Ruiz D., 2002. A Chebyshev-based two-stage iterative method as an alternative to the direct solution of linear systems. RAL-TR-2002-021. Download Postscript file.
  9. Arioli M. and Manzini G. 2005, MI31: a conjugate gradient algorithm implementation with energy-norm stopping criteria. RAL-TR-2005-004
  10. Arioli M., 2008. Roundoff error analysis of orthogonal factorizations of upper Hessenberg rectangular matrices. RAL-TR-2008-004. Download PDF file
 
 

Proceedings


  1. Arioli M., Duff I. S., Noailles J., and Ruiz D., 1990. Comparison between block Cimmino and block SSOR algorithms for solving linear systems in a parallel environment. Report TR/89/11, CERFACS. Reprint from the "Proceedings of the conference Supercomputing Tools for Science and Engineering", Pisa 1989, Franco Angeli, pp 47-54.
  2. Arioli M., Duff I. S., Ruiz D., and Sadkane M., 1992. Techniques for accelerating the block Cimmino method. In "Proceedings of the Fifth Siam Conference on Parallel Processing for Scientific Computing" , J. Dongarra, ed., SIAM, pp 98--104.
  3. Arioli M., Codenotti B., and Fassino C., 1992. Error analysis of three methods for computing the matrix exponential. Report TR/92/PA/87 CERFACS. ERCIM workshop on Numerical Linear Algebra, Software Quality Principles and Techniques, Theoretical and Experimental Aspects of Knowledge Representation, Pisa, 1992.
  4. Arioli M., Drummond A., Duff I. S., and Ruiz D., 1994. Parallel block iterative solvers for heterogeneous computing environments. "Algorithms and parallel VLSI architectures III, Proceedings of the international workshop" M. Moonen et al. (eds.), Elsevier, 1994. Download PDF file
  5. Arioli M., Drummond A., Duff I. S., and Ruiz D., 1994. A parallel scheduler for block iterative solvers in heterogeneous computing environments. Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing, Ed.s D. H. Bailey et. al., SIAM, 1995,
  6. Arioli M. and Ruiz D., 1995. Block Conjugate Gradient with Subspace Iteration for Solving Linear Systems. In: S. Margenov and P. Vassilevski (eds.), Iterative Methods in Linear Algebra, II. Proceedings of the Second IMACS Symposium on Iterative Metohds in Linear Algebra, Blagoevgrad, Bulgaria, June 17-20, 1995, pp. 64-79.
  7. Arioli M. and Manzini G., 2000. Null Space Algorithms for Solving Augmented Systems arising in the the Mixed Finite Element Approximation of Saddle Point Problems. CSCC 2000, MCP 2000, MCME 2000 Proceeding, ISBN:960-8052-19-X, N. E. Mastorakis (Ed.) pp 2851-2856. Download Postscript file.
  8. Arioli M., 2003. Backward Error Analysis and Stopping Criteria for Krylov Space Methods. In:  D. Griffiths and G. Alistair Watson (eds). Numerical Analysis 2003. Proceeding of the 20th Biennial Conference, 24-27 June 2003, Dundee, Scotland, UK. Invited talk.
  9. Arioli M. and Loghin D., 2008. Matrix square-root preconditioners for the Steklov-Poincare operator. “Series on Mathematical Modelling of Environmental and Life Sciences Problems”, Proceedings of the 6th  workshop, September 2007, Costanta, Romania, Academiei Romane. Download PDF file