1,720,981 research outputs found
Parallel algorithms for matrix polynomial division
No full textAbstractIn this paper, several algorithms for the matrix polynomial division are taken into consideration. Such algorithms represent extensions of known parallel algorithms for the scalar polynomial division with remainder. The interest resides in the comparison of the parallel computational cost of these algorithms in the general non scalar case
Theoretical and practical efficiency measures for symmetric interpolatory quadrature formulas
No full textStability of the Levinson algorithm for Toeplitz-like Systems
No full textNumerical stability of the Levinson algorithm, generalized for Toeplitz-
like systems, is studied. Arguments based on the analytic results of an
error analysis for floating point arithmetic produce an upper bound on
the norm of the residual vector, which grows exponentially with respect
to the size of the problem. The base of such an exponential function
can be small for diagonally dominant Toeplitz-like matrices. Numerical
experiments show that, for these matrices, Gaussian elimination by row
and the Levinson algorithm have residuals of the same order of magnitude.
As expected, the empirical results point out that the theoretical bound is
too pessimistic
Stopping rules for iterative methods in nonnegatively constrained deconvolution
No full textWe consider the two-dimensional discrete nonnegatively constrained deconvolution problem, whose goal is to reconstruct an object x^@? from its image b obtained through an optical system and affected by noise. When the large size of the problem prevents regularization through a direct method, iterative methods enjoying the semi-convergence property, coupled with suitable strategies for enforcing nonnegativity, are suggested. For these methods an accurate detection of the stopping index is essential. In this paper we analyze various stopping rules and, with the aid of a large experimentation, we test their effect on three different widely used iterative regularizing methods
A Framework for Studying the Regularizing Properties of Krylov Subspace Methods
No full textKrylov subspace iterative methods have recently received considerable
attention as regularizing techniques for solving linear systems with a coefficient matrix of ill-determined rank and a right-hand side vector perturbed by noise. For many of them little is known from this point of view. In this paper the regularizing properties of some methods of Krylov type (CGLS, GMRES, QMR, CGS, BiCG, Bi-CGSTAB) are examined. CGLS, for which a theoretical analysis is
available, is taken as reference method. Tools for measuring the regularization efficiency and the consistency with the discrepancy principle are introduced. An extensive experimentation validates
the proposed measures for the studied methods
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