Alternatives for parallel Krylov subspace basis computation

Numerical methods related to Krylov subspaces are widely used in large sparse numerical linear algebra. Vectors in these subspaces are manipulated via their representation onto orthonormal bases. Nowadays, on serial computers, the method of Arnoldi is considered as a reliable technique for constructing such bases. However, although easily parallelizable, this technique is not as scalable as expected for communications. In this work we examine alternative methods aimed at overcoming this drawback. Since they retrieve upon completion the same information as Arnoldi's algorithm does, they enable us to design a wide family of stable and scalable Krylov approximation methods for various parallel environments. We present timing results obtained from their implementation on two distributed-memory multiprocessor supercomputers: the Intel Paragon and the IBM Scalable POWERparallel SP2. (C) 1997 by John Wiley & Sons, Ltd.

Antarctic tourists, wildlife and the environment: Attractions and reactions to Antarctica

Provides background on the development and nature of Antarctic tourism and associated environmental issues, as well as agreements and regulations affecting environmental management in Antarctica. Following an outline of the survey methodology and provision of information on the socioeconomic profiles of the respondents, results of a survey of Antarctic tourists on the Russian registered ship the ‘Akademik Ioffe’ are reported. The importance of Antarctic wildlife as an attraction for these Antarctic tourists is then given particular attention. The study considers amongst other things how important Antarctic wildlife was in convincing these tourists to undertake their trip to Antarctica, the importance to the tourists of seeing different species of wildlife and the relative importance of wildlife compared with other attractions of the tour to Antarctica. Views both prior to and following visits to Antarctica are given. The views of the tourists about selected environmental issues involving Antarctica were canvassed. These are reported and discussed. Amongst the subjects discussed is whether the sampled tourists favour an expansion in tourism to Antarctica and why. An overall assessment completes the study.

Antarctic tourists: A case study of their evaluation of Antarctic wildlife and environmental issues

Reports the results of surveys of Antarctic cruise ship passengers on the ‘Akademik Ioffe’ who undertook their Antarctic journey in January 2003. The prime purposes of the surveys were to determine the socio-economic profile of these travellers, evaluate the importance of Antarctic wildlife for their travel, their attitude to Antarctic wildlife conservation as well as environmental issues involving Antarctica, both prior to their tourist visit to Antarctica and following it. This paper reports on the socio-economic profile of respondents, their willingness to pay for their Antarctic trip, and their knowledge of Antarctica. The comparative importance of Antarctic wildlife as a factor motivating respondents to undertake their journey is assessed and the evaluation of travellers following their Antarctic visit is considered. The relative importance of different Antarctic wildlife species is taken into account as well as Antarctic attractions other than wildlife. The attitudes of respondents to several environmental issues involving Antarctica, (eg. the commercial use of its natural resources and global environmental change impacting on Antarctica) are canvassed and summarised. In conclusion, the relevance of the survey results for Antarctic conservation are discussed. Particular attention is given to the question of whether Antarctic tourism favours or threatens Antarctic nature conservation.

Expokit: A software package for computing matrix exponentials

Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear ODEs with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.