The Shell model Monte Carlo (SMMC) method [1] was developed as an alternative to direct diagonalization in order to study low-energy nuclear properties. It was successfully applied to nuclear problems where large model spaces made diagonalization impractical. One calculates the thermal canonical expectation values of observables of few-body operators by representing the imaginary-time many-body...

We describe a new method of computing functions of highly non-normal matrices, by using the concept of approximate diagonalization. We formulate a conjecture about its efficiency, and provide both theoretical and numerical evidence in support of the conjecture. We apply the method to compute arbitrary real powers of highly non-normal matrices. 1. Introduction. Let A be a non-normal n × n matrix...

An element $u$ of a ring $R$ is called \textsl{unipotent} if $u-1$ is
 nilpotent. Two elements $a,b\in R$ are \textsl{unipotent equivalent}
 there exist unipotents $p,q\in such that $b=q^{-1}ap$. square
 matrices $A,B$ \textsl{strongly unipotent equivalent} there
 triangular $P,Q$ with $B=Q^{-1}AP$.
 In this paper, over commutative reduced rings, we characterize the mat...

We present exact and stochastic diagonalization results for a BCS-reduced Hubbard model. The kinetic Hamiltonian is the same as in the single band Hubbard model with additional next nearest neighbor hopping. The interaction of this model is designed to inhibit superconductivity in the dx2−y2 channel. The ground state of this model is studied by exact and stochastic diagonalization technique. We...