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- Claude Brezinski, Michela Redivo-Zaglia, Giuseppe Rodriguez, Sebastiano Seatzu
- Numerische Mathematik
- 2003

Summary. When a system of linear equations is ill-conditioned, regularization techniques provide a quite useful tool for trying to overcome the numerical inherent difficulties: the ill-conditioned… (More)

- Claude Brezinski, Giuseppe Rodriguez, Sebastiano Seatzu
- Numerical Algorithms
- 2008

In this paper, we discuss several (old and new) estimates for the norm of the error in the solution of systems of linear equations, and we study their properties. Then, these estimates are used for… (More)

- Tim N. T. Goodman, Charles A. Micchelli, Giuseppe Rodriguez, Sebastiano Seatzu
- Adv. Comput. Math.
- 1997

We analyse the performance of five numerical methods for factoring a Laurent polynomial, which is positive on the unit circle, as the modulus squared of a real algebraic polynomial. It is found that… (More)

Starting from the scattering data, the initial-value problem for the focusing nonlinear Schrödinger equation is solved numerically by following the path of the inverse scattering transform. The… (More)

It is shown that, under certain conditions, orthonormalizing the positive integer shifts of an exponentially decaying function on the half line by the Gram-Schmidt process leads to a limiting profile… (More)

In this article the Marchenko integral equations leading to the solution of the inverse scattering problem for the 1-D Schrödinger equation on the line are solved numerically. The linear system… (More)

- Tim N. T. Goodman, Charles A. Micchelli, Giuseppe Rodriguez, Sebastiano Seatzu
- SIAM J. Matrix Analysis Applications
- 2000

We study the Cholesky factorization of certain bi-infinite matrices and related finite matrices. These results are applied to show that if the uniform translates of a suitably decaying multivariate… (More)

- Claude Brezinski, Giuseppe Rodriguez, Sebastiano Seatzu
- Numerical Algorithms
- 2008

The a posteriori estimate of the errors in the numerical solution of ill-conditioned linear systems with contaminated data is a complicated problem. Several estimates of the norm of the error have… (More)

- Claude Brezinski, Michela Redivo-Zaglia, Giuseppe Rodriguez, Sebastiano Seatzu
- Numerische Mathematik
- 1998

Summary. In this paper, the regularized solutions of an ill–conditioned system of linear equations are computed for several values of the regularization parameter
$\lambda$. Then, these solutions… (More)

- Lothar Reichel, Giuseppe Rodriguez, Sebastiano Seatzu
- Numerical Algorithms
- 2008

The computation of an approximate solution of linear discrete ill-posed problems with contaminated data is delicate due to the possibility of severe error propagation. Tikhonov regularization seeks… (More)