Restarted GMRES methods augmented with approximate eigenvectors are widely used for solving large sparse linear systems. Recently a new scheme of augmenting with error approximations is proposed. The main aim of this paper is to develop a restarted GMRES method augmented with the combination of harmonic Ritz vectors and error approximations. We demonstrate that the resulted combination method c...

This article is devoted to the numerical solution of large-scale quadratic eigenvalue problems. Such problems arise in a wide variety of applications, such as the dynamic analysis of structural mechanical systems, acoustic systems, fluid mechanics, and signal processing. We first introduce a generalized second-order Krylov subspace based on a pair of square matrices and two initial vectors and ...

Postoperative hematoma is a rare but potentially life-threatening and unpredictable complication of thyroid surgery. We report two cases of very late postoperative bleeding occurring on the 13th postoperative day in patients treated with low-molecular-weight heparin and acenocoumarol. Patient 1 was readmitted with complaints of progressive anterior neck swelling and bleeding from the cervical w...

A matrix-free algorithm, IRLANB, for the efficient computation of the smallest singular triplets of large and possibly sparse matrices is described. Key characteristics of the approach are its use of Lanczos bidiagonalization, implicit restarting, and harmonic Ritz values. The algorithm also uses a deflation strategy that can be applied directly on Lanczos bidiagonalization. A refinement postpr...

In this paper, we propose an implicitly restarted block Lanczos bidiagonalization (IRBLB) method for computing a few extreme or interior singular values and associated right and left singular vectors of a large matrix A. Our method combines the advantages of a block routine, implicit shifting, and the application of Leja points as shifts in the accelerating polynomial. The method neither requir...

Several local search algorithms for real-valued domains (axis parallel line search, Nelder-Mead simplex search, Rosenbrock's algorithm, quasi-Newton method, NEWUOA, and VXQR) are described and thoroughly compared in this article, embedding them in a multi-start method. Their comparison aims (1) to help the researchers from the evolutionary community to choose the right opponent for their algori...

Methods We report a case of a 47-year-old woman, with diagnosis of HIV infection since 2009 (HLA B5701 negative) that started ARVT in 2011. On the 2nd day of treatment with Tenofovir, Emtricitabine and Nevirapine she developed pruritic exanthema and palpebral edema. Two weeks later the Infecciologist discontinued ARVT and prescribed AH (antihistamines) and CS (oral corticosteroids) with symptom...