− A new inverse scattering method is assessed against some of the real input data measured by the Institut Fresnel, Marseille, France. The method is based on the application of an Inexact-Newton method to the Lippmann-Schwinger integral equation of the inverse scattering problem within the second-order Born approximation. The regularization properties of the approach are evaluated by considerin...

In this paper we study nonmonotone globalization techniques, in connection with finite-difference inexact Newton-GMRES methods, for solving large-scale systems of nonlinear equations in the case that the Jacobian matrix is not available. We first define a globalization scheme, which combines nonmonotone watchdog rules and nonmonotone derivative-free line searches, and we prove its global conver...

A hybrid HS and PRP type conjugate gradient method for smooth optimization is presented, which reduces to the classical RPR or HS method if exact linear search is used and converges globally and R-linearly for nonconvex functions with an inexact backtracking line search under standard assumption. An inexact version of the proposed method which admits possible approximate gradient or/and approxi...

This paper considers the inexact Barzilai-Borwein algorithm applied to saddle point problems. To this aim, we study the convergence properties of the inexact Barzilai-Borwein algorithm for symmetric positive definite linear systems. Suppose that gk and g̃k are the exact residual and its approximation of the linear system at the k-th iteration, respectively. We prove the R-linear convergence of t...

In this article, a new inexact alternating direction method(ADM) is proposed for solving a class of variational inequality problems. At each iteration, the new method firstly solves the resulting subproblems of ADM approximately to generate an temporal point x̃, and then the multiplier y is updated to get the new iterate y. In order to get x, we adopt a new descent direction which is simple comp...

This paper studies convergence analysis of a preconditioned inexact Uzawa method for nondi erentiable saddle-point problems. The SOR-Newton method and the SOR-BFGS method are special cases of this method. We relax the Bramble– Pasciak–Vassilev condition on preconditioners for convergence of the inexact Uzawa method for linear saddle-point problems. The relaxed condition is used to determine the...

Inexact search is a difficult and time-consuming task with widespread application. Acceleration of inexact search could have tremendous impact upon fields such as chemistry, meteorology, and even bioinformatics. Field-programmable gate arrays provide a means by which to accelerate this process. We demonstrate the acceleration of inexact search using the BurrowsWheeler transform on FPGAs using t...

1:30 Inexact Solves in Interpolatory Model Reduction, SERKAN GUGERCIN, CHRISTOPHER BEATTIE, AND SARAH WYATT (Department of Mathematics). We expand upon the work of Beattie and Gugercin, who examined the role of inexact solves in the interpolation-based model reduction setting. We show the effect of inexact solves in one-sided and two-sided interpolation-based reduction as well as for the optima...

The R5RS specification of numerical operations leads to unportable and intransparent behavior of programs. Specifically, the notion of “exact/inexact numbers” and the misleading distinction between “real” and “rational” numbers are two primary sources of confusion. Consequently, the way R5RS organizes numbers is significantly less useful than it could be. Based on this diagnosis, we propose to ...

For any continuous bilinear form defined on a pair of Hilbert spaces satisfying the compatibility Ladyshenskaya-Babušca-Brezzi condition, symmetric Schur complement operators can be defined on each of the two Hilbert spaces. In this paper, we find bounds for the spectrum of the Schur operators only in terms of the compatibility and continuity constants. In the light of the new spectral results ...