Related papers: A faster multipole Legendre-Chebyshev transform
Lagrangian coherent structures (LCS) in fluid flows appear as co-dimension one ridges of the finite time Lyapunov exponent (FTLE) field. In three- dimensions this means two-dimensional ridges. A fast algorithm is presented here to locate…
The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and…
Anderson acceleration (or Anderson mixing) is an efficient acceleration method for fixed point iterations $x_{t+1}=G(x_t)$, e.g., gradient descent can be viewed as iteratively applying the operation $G(x) \triangleq x-\alpha\nabla f(x)$. It…
Machine learning methods have nowadays become easy-to-use tools for constructing high-dimensional interatomic potentials with ab initio accuracy. Although machine learned interatomic potentials are generally orders of magnitude faster than…
A parallel algorithm for computing the finite difference solution to the elliptic equations with non-separable variables is presented. The resultant matrix is symmetric positive definite, thus the preconditioning conjugate gradient or the…
Legendre orthogonal moments have been widely used in the field of image analysis. Because their computation by a direct method is very time expensive, recent efforts have been devoted to the reduction of computational complexity.…
Methods for stochastic trace estimation often require the repeated evaluation of expressions of the form $z^T p_n(A)z$, where $A$ is a symmetric matrix and $p_n$ is a degree $n$ polynomial written in the standard or Chebyshev basis. We show…
The paper describes two iterative algorithms for solving general systems of M simultaneous linear algebraic equations (SLAE) with real matrices of coefficients. The system can be determined, underdetermined, and overdetermined. Linearly…
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…
This article presents the novel breakthrough general purpose algorithm for large scale optimization problems. The novel algorithm is capable of achieving breakthrough speeds for very large-scale optimization on general purpose laptops and…
Solving symmetric positive semidefinite linear systems is an essential task in many scientific computing problems. While Jacobi-type methods, including the classical Jacobi method and the weighted Jacobi method, exhibit simplicity in their…
We study multiproposal Markov chain Monte Carlo algorithms, such as Multiple-try or generalised Metropolis-Hastings schemes, which have recently received renewed attention due to their amenability to parallel computing. First, we prove that…
Nowadays, low-rank approximations of matrices are an important component of many methods in science and engineering. Traditionally, low-rank approximations are considered in unitary invariant norms, however, recently element-wise…
Convolutional neural networks are constructed with massive operations with different types and are highly computationally intensive. Among these operations, multiplication operation is higher in computational complexity and usually requires…
Current trends in parallel processors call for the design of efficient massively parallel algorithms for scientific computing. Parallel algorithms for Monte Carlo simulations of thermodynamic ensembles of particles have received little…
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…
The growing amount of high dimensional data in different machine learning applications requires more efficient and scalable optimization algorithms. In this work, we consider combining two techniques, parallelism and Nesterov's…
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…
We present a fast algorithm for generating Laguerre diagrams with cells of given volumes, which can be used for creating RVEs of polycrystalline materials for computational homogenisation, or for fitting Laguerre diagrams to EBSD or XRD…
Standard discretization techniques for boundary integral equations, e.g., the Galerkin boundary element method, lead to large densely populated matrices that require fast and efficient compression techniques like the fast multipole method…