We also demonstrate situations where the suggested PSD-like schemes can be preferable to the optimal PMINRES iteration.Grazing-incidence small-angle X-ray scattering (GISAXS) is an important technique in the characterization of samples at the nanometre scale.The resulting algorithm can be utilized in a 'spectrum-slicing' approach whereby a very large number of eigenvalues and associated eigenvectors of the matrix are computed by extracting eigenpairs located in different sub-intervals independently from one another.Mature applications such as fluid catalytic cracking and hydrocracking rely critically on early zeolite structures.The approaching end of traditional CMOS technology scaling that up until now followed Moore's law is coming to an end in the next decade.However, the DOE has come to depend on the rapid, predictable, and cheap scaling of computing performance to meet mission needs for scientific theory, large scale experiments, and national security.

This paper describes a technique for tackling this problem by combining a Thick-Restart version of the Lanczos algorithm with deflation ('locking') and a new type of polynomial filters obtained from a least-squares technique.

The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator.

A resolution-of-the-identity approximation renders the primitive one- and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices.

Search direction randomization for accelerating this algorithm is discussed.

Our primary goal is to bridge the theoretical gap between the optimal (PMINRES) and PSD-like methods for solving symmetric indefinite systems.

This paper describes a technique for tackling this problem by combining a Thick-Restart version of the Lanczos algorithm with deflation ('locking') and a new type of polynomial filters obtained from a least-squares technique.

The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator.

A resolution-of-the-identity approximation renders the primitive one- and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices.

Search direction randomization for accelerating this algorithm is discussed.

Our primary goal is to bridge the theoretical gap between the optimal (PMINRES) and PSD-like methods for solving symmetric indefinite systems.

Our approach integrates compact models of low-level characteristics of the emerging technologies to inform higher-level simulation models to evaluate their responsiveness to application requirements.