Browsing by Author "Rojas, Marielba"

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    A Large-Scale Trust-Region Approach to the Regularization of Discrete Ill-Posed Problems
    (1998-05) Rojas, Marielba
    We consider the problem of computing the solution of large-scale discrete ill-posed problems when there is noise in the data. These problems arise in important areas such as seismic inversion, medical imaging and signal processing. We pose the problem as a quadratically constrained least squares problem and develop a method for the solution of such problem. Our method does not require factorization of the coefficient matrix, it has very low storage requirements and handles the high degree of singularities arising in discrete ill-posed problems. We present numerical results on test problems and an application of the method to a practical problem with real data.
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    A large-scale trust-region approach to the regularization of discrete ill-posed problems
    (1999) Rojas, Marielba; Sorensen, Danny C.
    We consider the problem of computing the solution of large-scale discrete ill-posed problems when there is noise in the data. These problems arise in important areas such as seismic inversion, medical imaging and signal processing. We pose the problem as a quadratically constrained least squares problem and develop a method for the solution of such problem. Our method does not require factorization of the coefficient matrix, it has very low storage requirements and handles the high degree of singularities arising in discrete ill-posed problems. We present numerical results on test problems and an application of the method to a practical problem with real data.
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    A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem
    (1999-09) Rojas, Marielba; Santos, Sandra A.; Sorensen, Danny C.
    We present a matrix-free algorithm for the large-scale trust-region subproblem. Our algorithm relies on matrix-vector products only and does not require matrix factorizations. We recast the trust-region subproblem as a parameterized eigenvalue problem and compute an optimal value for the parameter. We then find the optimal solution of the trust-region subproblem from the eigenvectors associated with two of the smallest eigenvalues of the parameterized eigenvalue problem corresponding to the optimal parameter. The new algorithm uses a different interpolating scheme than existent methods and introduces a unified iteration that naturally includes the so-called hard case. We show that the new iteration is well defined and convergent at a superlinear rate. We present computational results to illustrate convergence properties and robustness of the method.
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    A Trust-Region Approach to the Regularization of Large-Scale Discrete Ill-Posed Problems
    (1999-12) Rojas, Marielba; Sorensen, Danny C.
    We consider the solution of large-scale least squares problems where the coefficient matrix comes from the discretization of an ill-posed operator and the right-hand size contains noise. Special techniques known as regularization methods are needed to treat these problems in order to control the effect of the noise on the solution. We pose the regularization problem as a trust-region subproblem and solve it by means of a recently developed method for the large-scale trust-region subproblem. We present numerical results on test problems, an inverse interpolation problem with real data, and a model seismic inversion problem with real data.