相关论文: Spectral functions and time evolution from the Che…

We present an expansion of a many-body correlation function in a sum of pseudomodes -- exponents with complex frequencies that encompass both decay and oscillations. The pseudomode expansion emerges in the framework of the Heisenberg…

By observing the equivalence of assertions on determining the jump of a function by its differentiated or integrated Fourier series, we generalize a previous result of Kvernadze, Hagstrom and Shapiro to the whole class of functions of…

We present a one-step algorithm that solves the Maxwell equations for systems with spatially varying permittivity and permeability by the Chebyshev method. We demonstrate that this algorithm may be orders of magnitude more efficient than…

This work proposes the extended functional tensor train (EFTT) format for compressing and working with multivariate functions on tensor product domains. Our compression algorithm combines tensorized Chebyshev interpolation with a low-rank…

Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often…

As a phase space language for quantum mechanics, the Wigner function approach bears a close analogy to classical mechanics and has been drawing growing attention, especially in simulating quantum many-body systems. However, deterministic…

Chebfun and related software projects for numerical computing with functions are based on the idea that at each step of a computation, a function $f(x)$ defined on an interval $[a,b]$ is "rounded" to a prescribed precision by constructing a…

We study the long-time behavior of solutions to the Schr\"odinger equation with a repulsive Coulomb potential on $\mathbb{R}^3$ for spherically symmetric initial data. Our approach involves computing the distorted Fourier transform of the…

An accurate treatment of electronic spectra in large systems with a technique such as time dependent density functional theory (TDDFT) is computationally challenging. Due to the Nyquist sampling theorem, direct real time simulations must be…

We develop a spectral method to solve the heat equation in a closed cylinder, achieving a quasi-optimal $\mathcal{O}(N\log N)$ complexity and high-order, spectral accuracy. The algorithm relies on a Chebyshev--Chebyshev--Fourier (CCF)…

In this paper we detail the reformulation and rewrite of core functions in the spBayes R package. These efforts have focused on improving computational efficiency, flexibility, and usability for point-referenced data models. Attention is…

Time evolution is formulated and discussed in the framework of Schroeder's functional equation. The proposed method yields smooth, continuous dynamics without the prior need for local propagation equations.

The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data…

We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is…

One of the most accurate methods for solving the time-dependent Schr\"{o}dinger equation uses a combination of the dynamic Fourier method with the split-operator algorithm on a tensor-product grid. To reduce the number of required grid…

Numerical simulation of stochastic differential equations over long time intervals poses significant computational challenges. In this paper, we propose a novel recursive polynomial chaos evolution method that achieves model reduction…

In convex optimization, continuous-time counterparts have been a fruitful tool for analyzing momentum algorithms. Fewer such examples are available when the function to minimize is non-convex. In several cases, discrepancies arise between…

We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimisation methods in the context of matrix product states. In particular, we introduce a new integration scheme for…

This article establishes a rigorous spectral framework for the mathematical analysis of SHAP values. We show that any predictive model defined on a discrete or multi-valued input space admits a generalized Fourier expansion with respect to…

We present the Fast Chebyshev Transform (FCT), a fast, randomized algorithm to compute a Chebyshev approximation of functions in high-dimensions from the knowledge of the location of its nonzero Chebyshev coefficients. Rather than sampling…