English
Related papers

Related papers: Two Chebyshev Spectral Methods for Solving Normal …

200 papers

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…

Computational Engineering, Finance, and Science · Computer Science 2019-03-21 Roel Van Beeumen , David B. Williams-Young , Joseph M. Kasper , Chao Yang , Esmond G. Ng , Xiaosong Li

We improve a recently developed expansion technique for calculating real frequency spectral functions of any one-dimensional model with short-range interactions, by postprocessing computed Chebyshev moments with linear prediction. This can…

Strongly Correlated Electrons · Physics 2014-08-06 Martin Ganahl , Patrik Thunström , Frank Verstraete , Karsten Held , Hans Gerd Evertz

In this paper, we design and analyze a novel spectral method for the subdiffusion equation. As it has been known, the solutions of this equation are usually singular near the initial time. Consequently, direct application of the traditional…

Numerical Analysis · Mathematics 2022-04-06 Chuanju Xu , Wei Zeng

The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of 2D scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary…

We propose a spectral method based on the implementation of Chebyshev polynomials to study a model of conservation laws on network. We avoid the Gibbs phenomenon near shock discontinuities by implementing a filter in the frequency space in…

Numerical Analysis · Mathematics 2023-05-26 Sabrina Francesca Pellegrino

In this letter, a matrix method is employed to study the scalar quasinormal modes of Kerr as well as Kerr-Sen black holes. Discretization is applied to transfer the scalar perturbation equation into a matrix form eigenvalue problem, where…

General Relativity and Quantum Cosmology · Physics 2017-08-02 Kai Lin , Wei-Liang Qian , Alan B. Pavan , Elcio Abdalla

This manuscript details the use of the rational Chebyshev transform for describing the transverse dynamics of high-power laser diodes, either broad area lasers, index guided lasers or monolithic master oscillator power amplifier devices.…

Optics · Physics 2014-07-03 J. Javaloyes , S. Balle

In this paper a family of fixed point algorithms for the numerical resolution of some systems of nonlinear equations is designed and analyzed. The family introduced here generalizes the Petviashvili method and can be applied to the…

Numerical Analysis · Mathematics 2013-11-12 J. Alvarez , A. Duran

We develop the effective non-Hermitian Hamiltonian approach for open systems with Neumann boundary conditions. The approach can be used for calculating the scattering matrix and the scattering function in open resonator-waveguide systems.…

Quantum Physics · Physics 2015-04-14 Dmitrii N. Maksimov , Almas F. Sadreev , Alina A. Lyapina , Artem S. Pilipchuk

We present a refinement of the Spectral Method by incorporating an optimization method into it and generalize it to two space dimensions. We then apply this Refined Spectral Method as an extremely accurate technique for finding the bound…

Mathematical Physics · Physics 2007-05-23 P. Pedram , M. Mirzaei , S. S. Gousheh

In one of the most important methods in Density Functional Theory - the Full-Potential Linearized Augmented Plane Wave (FLAPW) method - dense generalized eigenproblems are organized in long sequences. Moreover each eigenproblem is strongly…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-05-23 Mario Berljafa , Edoardo Di Napoli

A practical and simple stable method for calculating Fourier integrals is proposed, effective both at low and at high frequencies. An approach based on the fruitful idea of Levin, to use of the collocation method to approximate the slowly…

Numerical Analysis · Mathematics 2021-04-09 Leonid A. Sevastianov , Konstantin P. Lovetskiy , Dmitry S. Kulyabov

Hidden Markov Models (HMMs) can be accurately approximated using co-occurrence frequencies of pairs and triples of observations by using a fast spectral method in contrast to the usual slow methods like EM or Gibbs sampling. We provide a…

Machine Learning · Statistics 2012-03-29 Dean P. Foster , Jordan Rodu , Lyle H. Ungar

Anomaly detection in massive networks has numerous theoretical and computational challenges, especially as the behavior to be detected becomes small in comparison to the larger network. This presentation focuses on recent results in three…

Social and Information Networks · Computer Science 2014-12-16 Benjamin A. Miller , Nicholas Arcolano , Michael M. Wolf , Nadya T. Bliss

The propagation of sound waves in a horizontally stratified environment, a classic problem in ocean acoustics, has traditionally been calculated using normal modes. Most programs based on the normal mode model are discretized using the…

Computational Engineering, Finance, and Science · Computer Science 2021-07-29 Houwang Tu , Yongxian Wang , Qiang Lan , Wei Liu , Wenbin Xiao , Shuqing Ma

We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems. This…

Numerical Analysis · Mathematics 2016-12-12 Richard Mikael Slevinsky , Sheehan Olver

In this paper, we investigate the AMLI-cycle method and make two contributions. First, we revisit the AMLI-cycle using the Chebyshev polynomials and establish a theory for its uniform convergence, assuming the two-grid method converges…

Numerical Analysis · Mathematics 2025-06-17 Chunyan Niu , Yunhui He , Xiaozhe Hu

Beamforming is an imaging tool for the investigation of aeroacoustic phenomena and results in high dimensional data that is broken down to spectra by integrating spatial Regions Of Interest. This paper presents two methods that enable the…

Sound · Computer Science 2021-09-29 Armin Goudarzi , Carsten Spehr , Steffen Herbold

In this paper, we consider numerical homogenization of acoustic wave equations with heterogeneous coefficients, namely, when the bulk modulus and the density of the medium are only bounded. We show that under a Cordes type condition the…

Numerical Analysis · Mathematics 2008-05-05 Houman Owhadi , Lei Zhang

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…

Spectral Theory · Mathematics 2021-03-02 Matthew John Colbrook