Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT.

We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenval...

Fast Algorithms for Estimating the Absorption Spectrum within the Linear Response Time-dependent Density Functional Theory

In this paper, we present two iterative algorithms for approximating the absorption spectrum of molecules within the linear response of time-dependent density functional theory (TDDFT) framework. These methods do not attempt to compute eigenvalues or eigenvectors of the linear response matrix. They are designed to approximate the absorption spectrum as a function directly. They take advantage o...

Efficient algorithms for estimating the general linear model

Computationally efficient serial and parallel algorithms for estimating the general linear model are proposed. The sequential block-recursive algorithm is an adaptation of a known Givens strategy that has as a main component the Generalized QR decomposition. The proposed algorithm is based on orthogonal transformations and exploits the triangular structure of the Cholesky QRD factor of the vari...

A Model Order Reduction Algorithm for Estimating the Absorption Spectrum

The ab initio description of the spectral interior of the absorption spectrum poses both a theoretical and computational challenge for modern electronic structure theory. Due to the often spectrally dense character of this domain in the quantum propagator's eigenspectrum for medium-to-large sized systems, traditional approaches based on the partial diagonalization of the propagator often encoun...

Efficient Algorithms for Computing the beta-spectrum