Related papers: High-performance implementation of Chebyshev filte…
For a function that is analytic on and around an interval, Chebyshev polynomial interpolation provides spectral convergence. However, if the function has a singularity close to the interval, the rate of convergence is near one. In these…
We consider filtered subspace iteration for approximating a cluster of eigenvalues (and its associated eigenspace) of a (possibly unbounded) selfadjoint operator in a Hilbert space. The algorithm is motivated by a quadrature approximation…
This paper concerns the design of a multidimensional Chebyshev interpolation based method for a differential game theory problem. In continuous game theory problems, it might be difficult to find analytical solutions, so numerical methods…
Treating high dimensionality is one of the main challenges in the development of computational methods for solving problems arising in finance, where tasks such as pricing, calibration, and risk assessment need to be performed accurately…
Contour-integral-based rational filter leads to interior eigensolvers for non-Hermitian generalized eigenvalue problems. Based on Zolotarev's third problem, this paper proves the asymptotic optimality of the trapezoidal quadrature of the…
In this paper, a numerical method is proposed to calculate the eigenvalues of the Zakharov-Shabat system based on Chebyshev polynomials. A mapping in the form of tanh(ax) is constructed according to the asymptotic of the potential function…
This paper describes the software package Cucheb, a GPU implementation of the filtered Lanczos procedure for the solution of large sparse symmetric eigenvalue problems. The filtered Lanczos procedure uses a carefully chosen polynomial…
The bilateral filter is an edge-preserving smoother that has diverse applications in image processing, computer vision, computer graphics, and computational photography. The filter uses a spatial kernel along with a range kernel to perform…
This paper presents an algorithm to simulate Gaussian random vectors whose precision matrix can be expressed as a polynomial of a sparse matrix. This situation arises in particular when simulating Gaussian Markov random fields obtained by…
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.…
We propose an optimization algorithm to compute the optimal sensor locations in experimental design in the formulation of Bayesian inverse problems, where the parameter-to-observable mapping is described through an integral equation and its…
Quantum Krylov subspace diagonalization is a prominent candidate for early fault tolerant quantum simulation of many-body and molecular systems, but so far the focus has been mainly on computing ground-state energies. We go beyond this by…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
We present an efficient algorithm for calculating spectral properties of large sparse Hamiltonian matrices such as densities of states and spectral functions. The combination of Chebyshev recursion and maximum entropy achieves high energy…
In this paper, we investigate diagonal estimation for large or implicit matrices, aiming to develop a novel and efficient stochastic algorithm that incorporates adaptive parameter selection. We explore the influence of different eigenvalue…
In this study linear and nonlinear higher order singularly perturbed problems are examined by a numerical approach, the differential quadrature method. Here, the main idea is using Chebyshev polynomials to acquire the weighting coefficient…
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…
Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…
This paper proposes an efficient method for computing selected generalized eigenpairs of a sparse Hermitian definite matrix pencil $(A,B)$. Based on Zolotarev's best rational function approximations of the signum function and conformal…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…