The Kronecker product has a rich and very pleasing algebra that supports a wide range of
fast, elegant, and practical algorithms. Several trends in scientific computing suggest that …

In many large scale scientific or engineering computations, ranging from computing the
frequency response of a circuit to the earthquake response of a buildingto the energy levels …

We describe new algorithms of the locally optimal block preconditioned conjugate gradient
(LOBPCG) method for symmetric eigenvalue problems, based on a local optimization of a …

This dissertation focuses on efficiently forming reduced-order models for large, linear
dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reduced …

We present a technique for optimizing hundreds of thousands of variational parameters in
variational quantum Monte Carlo. By introducing iterative Krylov subspace solvers and by …

A short survey of some results on preconditioned iterative methods for symmetric eigenvalue
problems is presented. The survey is by no means complete and reflects the author's …

The Jastrow-modified antisymmetric geminal power (JAGP) ansatz in Hilbert space
successfully overcomes two key failings of other pairing theories, namely, a lack of inter-pair …

A method for computing a few eigenpairs of sparse symmetric matrices is presented and
analyzed that combines the power of preconditioning techniques with the efficiency of the …

The electronic and optical properties of strained semiconductor quantum wires and dots are
investigated theoretically, taking into account their shapes and chemical compositions in a …

Computer simulation is an indispensable research tool in modeling, understanding and
predicting nanoscale phenomena. However, the advanced computer codes used by …