Related papers: A Fast Algorithm for Quadrature by Expansion in Th…

An implementation of the fast multiple method (FMM) is performed for magnetic systems with long-ranged dipolar interactions. Expansion in spherical harmonics of the original FMM is replaced by expansion of polynomials in Cartesian…

The fast computation of large kernel sums is a challenging task, which arises as a subproblem in any kernel method. We approach the problem by slicing, which relies on random projections to one-dimensional subspaces and fast Fourier…

We present a proximal augmented Lagrangian based solver for general convex quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case…

In this paper, we develop fast multipole methods for 3D Helmholtz kernel in layered media. Two algorithms based on different forms of Taylor expansion of layered media Green's function are developed. A key component of the first algorithm…

We developed a fast numerical algorithm for solving the three dimensional vectorial Helmholtz equation that arises in electromagnetic scattering problems. The algorithm is based on electric field integral equations and is essentially a…

Fast computation of three-dimensional gravity and magnetic forward models is considered. Measurement data is assumed to be obtained on a uniform grid which is staggered with respect to the discretization of the parameter volume. Then, the…

Quantization is a proven effective method for compressing large language models. Although popular techniques like W8A8 and W4A16 effectively maintain model performance, they often fail to concurrently speed up the prefill and decoding…

In this paper, a fast multipole method (FMM) is proposed to compute long-range interactions of wave sources embedded in 3-D layered media. The layered media Green's function for the Helmholtz equation, which satisfies the transmission…

The Fast Multipole Method (FMM) offers an acceleration for pairwise interaction calculation, known as $N$-body problems, from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ with $N$ particles. This has brought dramatic increase in the capability of…

An accelerated polynomial expansion scheme to construct the density matrix in quantum mechanical molecular dynamics simulations is proposed. The scheme is based on recursive density matrix expansions, e.g. [Phys. Rev. B. 66 (2002), p.…

Fractional programming (FP) arises in various communications and signal processing problems because several key quantities in the field are fractionally structured, e.g., the Cram\'{e}r-Rao bound, the Fisher information, and the…

This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms. We develop a novel scheme that takes advantage of blocking and recomputation…

Neighborhood Preserving Embedding (NPE) is an important linear dimensionality reduction technique that aims at preserving the local manifold structure. NPE contains three steps, i.e., finding the nearest neighbors of each data point,…

We propose QPALM, a nonconvex quadratic programming (QP) solver based on the proximal augmented Lagrangian method. This method solves a sequence of inner subproblems which can be enforced to be strongly convex and which therefore admit a…

The convolution potential arises in a wide variety of application areas, and its efficient and accurate evaluation encounters three challenges: singularity, nonlocality and anisotropy. We introduce a fast algorithm based on a far-field…

Evaluation of pair potentials is critical in a number of areas of physics. The classicalN-body problem has its root in evaluating the Laplace potential, and has spawned tree-algorithms, the fast multipole method (FMM), as well as kernel…

The kernel-independent fast multipole method (KIFMM) proposed in [1] is of almost linear complexity. In the original KIFMM the time-consuming M2L translations are accelerated by FFT. However, when more equivalent points are used to achieve…

This paper initiates the study of quantum algorithms for matroid property problems. It is shown that quadratic quantum speedup is possible for the calculation problem of finding the girth or the number of circuits (bases, flats,…

We propose a Jacobi-style distributed algorithm to solve convex, quadratically constrained quadratic programs (QCQPs), which arise from a broad range of applications. While small to medium-sized convex QCQPs can be solved efficiently by…

Fast Multipole Methods (FMMs) based on the oscillatory Helmholtz kernel can reduce the cost of solving N-body problems arising from Boundary Integral Equations (BIEs) in acoustic or electromagnetics. However, their cost strongly increases…