QMR: A Quasi-Minimal Residual method for non-Hermitian linear systems

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. A novel BCG like approach is presented called the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 2

It is shown how the look-ahead Lanczos process (combined with a quasi-minimal residual QMR) approach) can be used to develop a robust black box solver for large sparse non-Hermitian linear systems. Details of an implementation of the resulting QMR algorithm are presented. It is demonstrated that the QMR method is closely related to the biconjugate gradient (BCG) algorithm; however, unlike BCG, the QMR algorithm has smooth convergence curves and good numerical properties. We report numerical experiments with our implementation of the look-ahead Lanczos algorithm, both for eigenvalue problem and linear systems. Also, program listings of FORTRAN implementations of the look-ahead algorithm and the QMR method are included

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices

The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. An implementation is presented of a look-ahead version of the Lanczos algorithm that, except for the very special situation of an incurable breakdown, overcomes these problems by skipping over those steps in which a breakdown or near-breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products as the standard Lanczos process without look-ahead

An implementation of the QMR method based on coupled two-term recurrences

The authors have proposed a new Krylov subspace iteration, the quasi-minimal residual algorithm (QMR), for solving non-Hermitian linear systems. In the original implementation of the QMR method, the Lanczos process with look-ahead is used to generate basis vectors for the underlying Krylov subspaces. In the Lanczos algorithm, these basis vectors are computed by means of three-term recurrences. It has been observed that, in finite precision arithmetic, vector iterations based on three-term recursions are usually less robust than mathematically equivalent coupled two-term vector recurrences. This paper presents a look-ahead algorithm that constructs the Lanczos basis vectors by means of coupled two-term recursions. Implementation details are given, and the look-ahead strategy is described. A new implementation of the QMR method, based on this coupled two-term algorithm, is described. A simplified version of the QMR algorithm without look-ahead is also presented, and the special case of QMR for complex symmetric linear systems is considered. Results of numerical experiments comparing the original and the new implementations of the QMR method are reported

Primary culture and mRNA analysis of human ovarian cells

Established cell lines are invaluable for studying cell and molecular biological questions. A variety of human ovarian cancer (OC) cell lines exist, however, most have acquired significant genetic alterations from their cells of origin, including deletion of important cell cycle regulatory genes. In order to analyze signaling events related to cell cycle control in human OC, we have modified existing protocols for isolating and culturing OC cells from patient ascites fluid and normal ovarian surface epithelial (OSE) cells from benign ovarian tissue sections. These cells maintain an epithelial phenotype and can be manipulated experimentally for several passages before cellular senescence. An example using TGFb1 treatment of OC cells to examine signaling and target gene activation is presented

Recent advances in Lanczos-based iterative methods for nonsymmetric linear systems

In recent years, there has been a true revival of the nonsymmetric Lanczos method. On the one hand, the possible breakdowns in the classical algorithm are now better understood, and so-called look-ahead variants of the Lanczos process have been developed, which remedy this problem. On the other hand, various new Lanczos-based iterative schemes for solving nonsymmetric linear systems have been proposed. This paper gives a survey of some of these recent developments

Política Ambiental da Embrapa Clima Temperado.

bitstream/CPACT-2010/12322/1/documento-268.pd

Eco-friendly fungicide based on chitosan and pecan nut oil: development and evaluation in anthracnose control.

Industrial processing of pecan nuts results in edible oil ? with fractions of fatty acids, polyphenols and phytosterols - that may be used for managing phytopathogens. Besides, chitosan may interfere with pathogen development directly and/or activate mechanisms of defense in plant tissues. This study aimed at developing a novel, natural and eco-friendly fungicide based on pecan nut oil immobilized in chitosan and at evaluating its activity against Colletotrichum gloeosporioides, an agent of anthracnose in guava trees and other fruit trees. Changes in the immobilized material exhibited at bands were identified by infrared spectroscopy. Additionally, micrographs by scanning electron microscopy (SEM) showed efficient changes in the immobilized material, by comparison with the polymer chitosan. Decreases in Colletotrichum gloeosporioides sporulation in vitro were 37% in the case of pecan nut oil immobilized in chitosan (IO) and 39% in the case of non-immobilized pecan nut oil (NIO). These results are positive because this fungus produces a large number of spores which may disseminate and survive on surfaces of plant tissues infected by anthracnose. Immobilization of pecan oil in chitosan showed benefits in the synthesis of a novel, stable and eco-friendly material which may be applied to guava trees to control anthracnose