Mario Arioli

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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 sparse(More)
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 efficient(More)
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 error(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 H−1( ), we obtain a true(More)