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- Mario Arioli, Iain S. Duff, Joseph Noailles, Daniel Ruiz
- SIAM J. Scientific Computing
- 1992

- Ilaria Perugia, Valeria Simoncini, Mario Arioli
- SIAM J. Scientific Computing
- 1999

- Mario Arioli
- SIAM J. Matrix Analysis Applications
- 2000

We present a roundoff error analysis of a null space method for solving quadratic programming minimization problems. This method combines the use of a direct QR factorization of the constraints with an iterative solver on the corresponding null space. Numerical experiments are presented which give evidence of the good performances of the algorithm on sparseâ€¦ (More)

Abstract. We study stopping criteria that are suitable in the solution by Krylov space based methods of linear and non linear systems of equations arising from the mixed and the mixed-hybrid finite-element approximation of saddle point problems. Our approach is based on the equivalence between the BabuÅ¡ka and Brezzi conditions of stability which allows usâ€¦ (More)

- Mario Arioli, Iain S. Duff, Serge Gratton, StÃ©phane Pralet
- SIAM J. Scientific Computing
- 2007

- Mario Arioli, Daniel Loghin
- SIAM J. Numerical Analysis
- 2009

We describe norm representations for interpolation spaces generated by finitedimensional subspaces of Hilbert spaces. These norms are products of integer and non-integer powers of the Grammian matrices associated with the generating pair of spaces for the interpolation space. We include a brief description of some of the algorithms which allow the efficientâ€¦ (More)

- Mario Arioli, Hans Z. Munthe-Kaas, L. Valdettaro
- Numerical Algorithms
- 1996

We analyze the stability of the Cooley-Tukey algorithm for the Fast Fourier Transform of ordern=2 k and of its inverse by using componentwise error analysis. We prove that the components of the roundoff errors are linearly related to the result in exact arithmetic. We describe the structure of the error matrix and we give optimal bounds for the total errorâ€¦ (More)

We show that, when solving a linear system with an iterative method, it is necessary to measure the error in the space in which the residual lies. We present examples of linear systems which emanate from the finite element discretization of elliptic partial differential equations, and we show that, when we measure the residual in Hâˆ’1( ), we obtain a trueâ€¦ (More)

- Mario Arioli, Lucia Baldini
- SIAM J. Matrix Analysis Applications
- 2001

- Mario Arioli, Iain S. Duff, Nicholas I. M. Gould, John K. Reid
- SIAM J. Scientific Computing
- 1990