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...

We present an algorithm for large-scale equality constrained optimization. The method is based on a characterization of inexact sequential quadratic programming (SQP) steps that can ensure global convergence. Inexact SQP methods are needed for large-scale applications for which the iteration matrix cannot be explicitly formed or factored and the arising linear systems must be solved using itera...

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 ...

When a quantity is measured, the outcome depends on several factors like the measuring system, the measurement procedure, the skill of the operator, the environment, and other effects. In case of inexact quantity the outcome may also depends on the uncertainty representation. Recently inexact numbers got a lot of attention from many researchers in different fields. In this paper, we have tried ...

We study the local convergence of several inexact numerical algorithms closely related to Newton’s method for the solution of a simple eigenpair of the general nonlinear eigenvalue problem T (λ)v = 0. We investigate inverse iteration, Rayleigh quotient iteration, residual inverse iteration, and the single-vector Jacobi-Davidson method, analyzing the impact of the tolerances chosen for the appro...