Related papers: Multi-Grid Lanczos
Global optimization is an active area of research in atomistic simulations, and many algorithms have been proposed to date. A prominent example is basin hopping Monte Carlo, which performs a modified Metropolis Monte Carlo search to explore…
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…
The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale parallel computation frameworks and has recently gained a lot of importance, especially in the context of classic graph problems.…
A theory is presented for a novel recursion method for O(N) ab initio tight-binding calculations. A long-standing problem of generalizing the recursion method to a non-orthogonal basis, which is a crucial step to make the recursion method…
Recent work has shown that the (block) Lanczos algorithm can be used to extract approximate energy spectra and matrix elements from (matrices of) correlation functions in quantum field theory, and identified exact coincidences between…
The computational effort in the calculation of Wilson fermion quark propagators in Lattice Quantum Chromodynamics can be considerably reduced by exploiting the Wilson fermion matrix structure in inversion algorithms based on the…
In this paper we generalise the results on eigenvalues and eigenvectors of unnormalized (combinatorial) Laplacian of two-dimensional grid presented by Edwards:2013 first to a grid graph of any dimension, and second also to other types of…
Lanczos-type algorithms are efficient and easy to implement. Unfortunately they breakdown frequently and well before convergence has been achieved. These algorithms are typically based on recurrence relations which involve formal orthogonal…
Lanczos-based methods have become standard tools for tasks involving matrix functions. Progress on these algorithms has been driven by several largely disjoint communities, resulting many innovative and important advancements which would…
Many fields of science and engineering require finding eigenvalues and eigenvectors of large matrices. The solutions can represent oscillatory modes of a bridge, a violin, the disposition of electrons around an atom or molecule, the…
This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…
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 :…
This paper introduces an efficient $\mathcal{O}(n)$ compute and memory complexity algorithm for globally optimal path planning on 2D Cartesian grids. Unlike existing marching methods that rely on approximate discretized solutions to the…
We propose a sparse grids based adaptive noise reduction strategy for electrostatic particle-in-cell (PIC) simulations. Our approach is based on the key idea of relying on sparse grids instead of a regular grid in order to increase the…
This dissertation develops hardware that automatically reduces the effective latency of accessing memory in both single-core and multi-core systems. To accomplish this, the dissertation shows that all last level cache misses can be…
Lattice Boltzmann method (LBM) is a promising approach to solving Computational Fluid Dynamics (CFD) problems, however, its nature of memory-boundness limits nearly all LBM algorithms' performance on modern computer architectures. This…
We present a completely unbiased and controlled numerical method to solve quantum impurity problems in d-dimensional lattices. This approach is based on a canonical transformation, of the Lanczos form, where the complete lattice Hamiltonian…
This paper revisits the error analysis of the Stochastic Lanczos Quadrature (SLQ) method for approximating the trace of matrix functions, with a specific focus on asymmetric Lanczos quadrature rules. We reexplain an existing theoretical…
We investigate the oblique Lanczos method recently put forward in arXiv:2406.20009 for analysing Euclidean correlators in lattice field theories and show that it is analytically equivalent to the well known Prony Generalised Eigenvalue…
We reformulate the Lanczos algorithm for quantum wave function propagation in terms of variational principle. By including some basis states of previous time steps into the variational subspace, the resultant accuracy increases by several…