Related papers: Krylov subspace methods for the Dirac equation
We study the universal properties of the Lanczos algorithm applied to finite-size many-body quantum systems. Focusing on autocorrelation functions of local operators and on their infinite-time behaviour at finite size, we conjecture that in…
A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant…
Quadratic minimization problems with orthogonality constraints (QMPO) play an important role in many applications of science and engineering. However, some existing methods may suffer from low accuracy or heavy workload for large-scale…
A deflated and restarted Lanczos algorithm to solve hermitian linear systems, and at the same time compute eigenvalues and eigenvectors for application to multiple right-hand sides, is described. For the first right-hand side, eigenvectors…
The Lanczos process constructs a sequence of orthonormal vectors v_m spanning a nested sequence of Krylov subspaces generated by a hermitian matrix A and some starting vector b. In this paper we show how to cheaply recover a secondary…
A new procedure is constructed by means of APS in APLAN language. The procedure solves the initial-value problem for linear differential equations of order $k$ with polynomial coefficients and regular singularity in the initialization point…
For the Hermitian inexact Rayleigh quotient iteration (RQI), the author has established new local general convergence results, independent of iterative solvers for inner linear systems. The theory shows that the method locally converges…
Partitioning a graph into three pieces, with two of them large and connected, and the third a small ``separator'' set, is useful for improving the performance of a number of combinatorial algorithms. This is done using the second…
We consider the massive Dirac equation in the non-extreme Kerr geometry in horizon-penetrating advanced Eddington-Finkelstein-type coordinates and derive a functional analytic integral representation of the associated propagator using the…
The computation of resistance distance is pivotal in a wide range of graph analysis applications, including graph clustering, link prediction, and graph neural networks. Despite its foundational importance, efficient algorithms for…
The growing availability and usage of low precision foating point formats has attracts many interests of developing lower or mixed precision algorithms for scientific computing problems. In this paper we investigate the possibility of…
In this paper we propose and analyze an algorithm for identifying spectral gaps of a real symmetric matrix $A$ by simultaneously approximating the traces of spectral projectors associated with multiple different spectral slices. Our method…
In this work we introduce a memory-efficient method for computing the action of a Hermitian matrix function on a vector. Our method consists of a rational Lanczos algorithm combined with a basis compression procedure based on rational…
Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the…
In this paper, we present an approach to deal with the dynamics of the Dirac equation with time-dependent electromagnetic potentials using the fourth-order compact time-splitting method ($S_\text{4c}$). To this purpose, the time-ordering…
In her seminal 1989 work, Greenbaum demonstrated that the results produced by the finite precision Lanczos algorithm after $k$ iterations can be interpreted as exact Lanczos results applied to a larger matrix, whose eigenvalues lie in small…
Polynomial Krylov subspace methods are among the most widely used methods for approximating $f(A)b$, the action of a matrix function on a vector, in particular when $A$ is large and sparse. When $A$ is Hermitian positive definite, the…
In this work, a fully implicit numerical approach based on space-time finite element method is presented to solve the Dirac equation in 1 (space) + 1 (time), 2 + 1, and 3 + 1 dimensions. We utilize PETSc/Tao library to implement our linear…
A common approach to approximating quadratic forms of matrix functions is to use a quadrature rule derived from the Lanczos process, known as a Lanczos quadrature. Although symmetric quadrature rules are computationally favorable, it has…
We analyze the Lanczos method for matrix function approximation (Lanczos-FA), an iterative algorithm for computing $f(\mathbf{A}) \mathbf{b}$ when $\mathbf{A}$ is a Hermitian matrix and $\mathbf{b}$ is a given vector. Assuming that $f :…