Related papers: Fast stray field computation on tensor grids
Radiative corrections to elastic electron-proton scattering are analyzed in effective field theory. A new factorization formula identifies all sources of large logarithms in the limit of large momentum transfer, $Q^2\gg m_e^2$. Explicit…
We present a fast direct algorithm for computing symmetric factorizations, i.e. $A = WW^T$, of symmetric positive-definite hierarchical matrices with weak-admissibility conditions. The computational cost for the symmetric factorization…
The development of accurate and fast numerical schemes for the five fold Boltzmann collision integral represents a challenging problem in scientific computing. For a particular class of interactions, including the so-called hard spheres…
Multilinear algebra kernel performance on modern massively-parallel systems is determined mainly by data movement. However, deriving data movement-optimal distributed schedules for programs with many high-dimensional inputs is a notoriously…
Micromagnetics depends on high-fidelity numerical methods for magnetization dynamics. This work proposes a third-order temporal accuracy scheme for the Landau-Lifshitz-Gilbert equation, addressing accuracy-efficiency trade-offs in existing…
The large-scale three-dimensional inversion of surface gravity / tensor gravity data is a very challenging numerical and practical problem, which is a highly physical memory usage, time-consuming computation and high precision for…
The recently developed matrix based Renyi's entropy enables measurement of information in data simply using the eigenspectrum of symmetric positive semi definite (PSD) matrices in reproducing kernel Hilbert space, without estimation of the…
Combining sum factorization, weighted quadrature, and row-based assembly enables efficient higher-order computations for tensor product splines. We aim to transfer these concepts to immersed boundary methods, which perform simulations on a…
An algorithm is given for explicitly computing Penrose diagrams for spacetimes of the form $ds^2 = -f(r)\, dt^2 + f(r)^{-1} \, dr^2 + r^2 \, d\Omega^2$. The resulting diagram coordinates are shown to extend the metric continuously and…
We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…
We propose a new practical algorithm for computing the Feigenbaum constants {\alpha} and {\delta}, having significantly lower time and space complexity than previously used methods. The algorithm builds upon well-known linear algebra…
Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
A simple algorithm and a computational program to numerically compute the electric field gradient and the concomitant quadrupolar nuclear splitting is developed for an arbitrary ionic crystal. The calculations are performed using a point…
The performance of numerical micromagnetic models is limited by the demagnetizing field computation, which typically accounts for the majority of the computation time. For magnetization dynamics simulations explicit evaluation methods are…
Recent developments in the design of magnetic confinement fusion devices have allowed the construction of exceptionally optimized stellarator configurations. The near-axis expansion in particular has proven to enable the construction of…
We proposed the tensor-input tree (TT) method for scalar-on-tensor and tensor-on-tensor regression problems. We first address scalar-on-tensor problem by proposing scalar-output regression tree models whose input variable are tensors (i.e.,…
We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment…
Suitable discretizations through tensor product formulas of popular multidimensional operators (diffusion or diffusion--advection, for instance) lead to matrices with $d$-dimensional Kronecker sum structure. For evolutionary Partial…
Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem…