Computing the eigenvalues and eigenvectors of a large sparse nonsymmetric matrix arises in many applications and can be a very computationally challenging problem. In this paper we propose the Augmented Block Householder Arnoldi (ABHA) method that combines the advantages of a block routine with an augmented Krylov routine. A public domain MATLAB code ahbeigs has been developed and numerical exp...

Quantum embedding based on the (one-electron reduced) density matrix is revisited by means of unitary Householder transformation. While being exact and equivalent to (but formally simpler than) theory (DMET) in non-interacting case, resulting transformed functional (Ht-DMFET) preserves, construction, single-particle character bath when electron correlation introduced. In Ht-DMFET, projected "im...

Successful exploitation of parallel computers depends to a large extent on the development of useful concepts which enable programmers to view different applications as variations of a common theme. Our most fundamental concepts, such as parallel processes and message communication, are embedded in programming languages. In other cases, we discover programming paradigms which can be used to sol...

An important geometric and linear algebraic problem denoted as vector orthogonalization, fundamental to handle contact detection and contact force descriptions in engineering applications, is here considered. The problem is to find a set of linearly independent vectors that span the entire R3 Euclidean space given only one of the base vectors. This paper contains the explanation on how theHouse...