The Effects of Rounding Error on an Algorithm for Downdating a Cholesky Factorization

Let the positive definite matrix A have a Cholesky factorizationA= R^TR. For a given vector xsuppose that ? =A - xx^T has a Choleskyfactorization ? = ^T.This paper considers an algorithm for computing from R and x and an extension for removing a row from the QR factorizationof a regression problem. It is shown that the algorithm is stablein the presence of rounding errors. However, it is also shownthat the matrix can be a very ill-conditioned function of R and x.     

On the perturbation of LU and Cholesky factors

In a recent paper, Chang and Paige have shown that the usualperturbation bounds for Cholesky factors can systematicallyoverestimate the errors. In this note we sharpen their resultsand extend them to the factors of the LU decomposition. Theresults are based on a new formula for the first-order termsof the error in the factors. ^* This report is available by anonymous ftp from thales.cs.umd.eduin the directory pub/reports.     

Comparison among three anion exchange chromatographic supports to capture erythropoietin from cell culture supernatant Lourdes

Affinity and ion exchange conventional chromatography have been used to capture erythropoietin (EPO) from mammalian cell culture supernatant. Currently, chromatographic adsorbent perfusion is available, however a limited number of applications have been found in the literature. In this work, three anion exchange chromatographic supports (gel, membrane and monolithic) were evaluated in the capture step of the recombinant erythropoietin purification process. The influences of load and flow rate on each support performance were analyzed. Also the purity of the EPO molecules was determined. A productivity analysis, as a decision tool for larger scale implementation, was done. As a conclusion, the evaluated supports are technically suitable to capture EPO with adequate recovery and good purity. However, the monolithic column admits high operating velocity, showing the highest adsorption capacity and productivity.