Robust and Efficient Numerical Linear Algebra Solvers and Applications in Quantum Mechanical Simulations

Optimization of large scale linear algebra computations is a long-standing problem in numerical analysis and scientific computing communities. In this pape, we describe our recent synergistic effort on the development of robust, accurate and efficient linear algebra techniques and applications to quantum mechanical simulation. We demonstrate the feasibility, through the use of newly developed linear algebra solvers, of 1000-electron quantum monte carlo simulations on a modern desktop machine. Such simulations would allow us to address important questions concerning the magnetic and transport properties of materials with strong electron-electron interactions. The results of robust and efficient linear algebra solvers have more general impact on forefront scientific computing beyond the application discussed here. As one example, the methodology described has close connections to problems in lattice gauge theory, dynamical mean field theory, and localization. 2000 Mathematics Subject Classification: 15A06, 65F05, 65F10, 65F40.