An augmented Lanczos algorithm for the efficient computation of a dot-product of a function of a large sparse symmetric matrix

The Lanczos algorithm is appreciated in many situations due to its speed. and economy of storage. However, the advantage that the Lanczos basis vectors need not be kept is lost when the algorithm is used to compute the action of a matrix function on a vector. Either the basis vectors need to be kept, or the Lanczos process needs to be applied twice. In this study we describe an augmented Lanczos algorithm to compute a dot product relative to a function of a large sparse symmetric matrix, without keeping the basis vectors.

Warranty and optimal reliability improvement through product development

For products sold with warranty, the warranty servicing cost can be reduced by improving product reliability through a development process. However, this increases the unit manufacturing cost. Optimal development must achieve a trade-off between these two costs. The outcome of the development process is uncertain and needs to be taken into account in the determination of the optimal development effort. The paper develops a model where this uncertainty is taken into account. (C) 2003 Elsevier Ltd. All rights reserved.