Related papers: High-performance implementation of Chebyshev filte…

In a recent paper we have suggested that the finite temperature density matrix can be computed efficiently by a combination of polynomial expansion and iterative inversion techniques. We present here significant improvements over this…

We present two new quantum algorithms for reaction-diffusion equations that employ the truncated Chebyshev polynomial approximation. This method is employed to numerically solve the ordinary differential equation emerging from the…

This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…

In this paper we introduce a new family of wavelets, named Chebyshev wavelets, which are derived from conventional first and second kind Chebyshev polynomials. Properties of Chebyshev filter banks are investigated, including orthogonality…

Kohn-Sham density functional theory calculations using conventional diagonalization based methods become increasingly expensive as temperature increases due to the need to compute increasing numbers of partially occupied states. We present…

The vertical modes of linearized equations of motion are widely used by the oceanographic community in numerous theoretical and observational contexts. However, the standard approach for solving the generalized eigenvalue problem using…

This paper addresses the challenges of designing mesh convolution neural networks for 3D mesh dense prediction. While deep learning has achieved remarkable success in image dense prediction tasks, directly applying or extending these…

Many numerical methods, such as tensor network approaches including density matrix renormalization group calculations, have been developed to calculate the extreme/ground states of quantum many-body systems. However, little attention has…

Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while…

This paper is concerned with computations of a few smaller eigenvalues (in absolute value) of a large extremely ill-conditioned matrix. It is shown that smaller eigenvalues can be accurately computed for a diagonally dominant matrix or a…

Many problems in linear algebra -- such as those arising from non-Hermitian physics and differential equations -- can be solved on a quantum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum…

A new algorithm to approximate Hermitian matrices by positive semidefinite Hermitian matrices based on modified Cholesky decompositions is presented. In contrast to existing algorithms, this algorithm allows to specify bounds on the…

This paper presents four novel domain decomposition algorithms integrated with nonlinear mapping techniques to address collocation-based solutions of eigenvalue problems involving sharp interfaces or steep gradients. The proposed methods…

Approximation theory plays a central role in numerical analysis, undergoing continuous evolution through a spectrum of methodologies. Notably, Lebesgue, Weierstrass, Fourier, and Chebyshev approximations stand out among these methods.…

We present a rational filter for computing all eigenvalues of a symmetric definite eigenvalue problem lying in an interval on the real axis. The linear systems arising from the filter embedded in the subspace iteration framework, are solved…

Logarithms of determinants of large positive definite matrices appear ubiquitously in machine learning applications including Gaussian graphical and Gaussian process models, partition functions of discrete graphical models, minimum-volume…

Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for…

The efficient compression of kernel matrices, for instance the off-diagonal blocks of discretized integral equations, is a crucial step in many algorithms. In this paper, we study the application of Skeletonized Interpolation to construct…

Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features…

We discuss two approaches to solving the parametric (or stochastic) eigenvalue problem. One of them uses a Taylor expansion and the other a Chebyshev expansion. The parametric eigenvalue problem assumes that the matrix $A$ depends on a…