We develop the gapped-filtering method, whereby a short Chebyshev expansion accurately represents density-matrix operator. The method optimizes coefficients to give correct density matrix at all energies except within gapped region where there are no eigenstates. Gapped filtering reduces number of required terms in compared traditional methods, as long one knows or can determine efficiently HOM...

In a recent paper we have suggested that the finite temperature density matrix can be computed efficiently by a combination of polynomial expansion and iterative inversion techniques. We present here significant improvements over this scheme. The original complex-valued formalism is turned into a purely real one. In addition, we use Chebyshev polynomials expansion and fast summation techniques....

The theorem proved here extends Chebyshev theory into what has previously been no man's land: functions which have an infinite number of bounded derivatives on the expansion interval [a, b] but which are singular at one endpoint. The Chebyshev series in l/x for all the familiar special functions fall into this category, so this class of functions is very important indeed. In words, the theorem ...

in chemical engineering, several processes are represented by singular boundary value problems. in general, classical numerical methods fail to produce good approximations for the singular boundary value problems. in this paper, chebyshev finite difference (chfd) method and dtm-pad´e method, which is a combination of differential transform method (dtm) and pad´e approximant, are applied for sol...

Martin Ganahl,1,* Patrik Thunström,2 Frank Verstraete,3,4 Karsten Held,2 and Hans Gerd Evertz1 1Institut für Theoretische Physik, Technische Universität Graz, 8010, Graz, Austria 2Institute of Solid State Physics, Vienna University of Technology, 1040, Vienna, Austria 3Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria 4Department of Physics and Astronomy, Ghent U...