Many problems in science and engineering require the solution of a long sequence of slowly changing linear systems. We propose and analyze two methods that significantly reduce the total number of matrix-vector products required to solve all systems. We consider the general case where both the matrix and right-hand side change, and we make no assumptions regarding the change in the right-hand sides. Furthermore, we consider general nonsingular matrices, and we do not assume that all matrices are pairwise close or that the sequence of matrices converges to a particular matrix. Our methods work well under these general assumptions, and hence form a significant advancement with respect to related work in this area. We can reduce the cost of solving subsequent systems in the sequence by recycling selected subspaces generated for previous systems. We consider two approaches that allow for the continuous improvement of the recycled subspace at low cost. We consider both Hermitian and non-Hermitian problems, and we analyze our algorithms both theoretically and numerically to illustrate the effects of subspace recycling. We also demonstrate the effectiveness of our algorithms for a range of applications from computational mechanics, materials science, and computational physics.

Twenty-six stocks of Pacific salmon and trout (Oncorhynchus spp.), representing evolutionary significant units (ESU), are listed as threatened or endangered under the Endangered Species Act (ESA) and six more stocks are currently being evaluated for listing. The ecological and economic consequences of these listings are large; therefore considerable effort has been made to understand and respond to these declining populations. Until recently, Pacific harbor seals (Phoca vitulina richardsi) on the west coast increased an average of 5% to 7% per year as a result of the Marine Mammal Protection Act of 1972 (Brown and Kohlman2). Pacific salmon are seasonally important prey for harbor seals (Roffe and Mate, 1984; Olesiuk, 1993); therefore quantifying and understanding the interaction between these two protected species is important for Morphobiologically sound management strategies. Because some Pacific salmonid species in a given area may be threatened or endangered, while others are relatively abundant, it is important to distinguish the species of salmonid upon which the harbor seals are preying. This study takes the first step in understanding these interactions by using molecular genetic tools for species-level identification of salmonid skeletal remains recovered from Pacific harbor seal scats.

Two teams — Computational Environment, and Computational Mathematics and Geometry — address research in the Computer Science Group. The target of our Computational Environment team is to provide the broad computational infrastructure necessary to support complex, large-scale simulations in general, and for rocket simulation in particular. Areas of research include parallel programming environments, compiler optimization and parallelization, parallel performance analysis and tools, parallel input/output, and visualization. Work in Computational Mathematics and Geometry focuses on the areas of linear solvers, mesh generation and adaptation, and interpolation between diverse discretizations.

Two teams, Computational Mathematics and Geometry, and Computational Environment, address research in Computer Science. The target of our Computational Environment team is to provide the broad computational infrastructure necessary to support complex, large-scale simulations in general, and for rocket simulation in particular. Areas of research include parallel programming environments, compiler optimization and parallelization, parallel performance analysis and tools, parallel input/output, and visualization. Work in Computational Mathematics and Geometry focuses on the areas of linear solvers, mesh generation and adaptation, and interpolation between diverse discretizations.