Related papers: Fast computation of analytic capacity
To achieve efficient and accurate long-time integration, we propose a fast, accurate, and stable high-order numerical method for solving fractional-in-space reaction-diffusion equations. The proposed method is explicit in nature and…
We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions using an extension of the recently introduced recursive strong skeletonization scheme. For problems that are not highly oscillatory, our…
Incomplete U-statistics have been proposed to accelerate computation. They use only a subset of the subsamples required for kernel evaluations by complete U-statistics. This paper gives a finite sample bound in the style of Bernstein's…
Kernel density estimation and kernel regression are powerful but computationally expensive techniques: a direct evaluation of kernel density estimates at $M$ evaluation points given $N$ input sample points requires a quadratic…
Kernel methods are extensively employed for nonlinear data clustering, yet their effectiveness heavily relies on selecting suitable kernels and associated parameters, posing challenges in advance determination. In response, Multiple Kernel…
In this note we propose an approach for a fast analytic determination of all possible eigenstates of rational GL(N|M) integrable spin chains of given not too large length, in terms of Baxter Q-functions. We observe that all exceptional…
Meshless methods are often used in numerical simulations of systems of partial differential equations (PDEs), particularly those which involve complex geometries or free surfaces. Here we present a novel compact scheme based on the local…
There are many interesting problems about the electrostatic potential of finitely many charges. We consider one of them concerning the intensity of the field, in other words, about the magnitude of the gradient of this potential. We want to…
We study eigenfunction localization for higher dimensional cat maps, a popular model of quantum chaos. These maps are given by linear symplectic maps in ${\mathrm{Sp}}(2g,\mathbb Z)$, which we take to be ergodic. Under some natural…
We present a new efficient analytical approximation scheme to two-point boundary value problems of ordinary differential equations (ODEs) adapted to the study of the derivative expansion of the exact renormalization group equations. It is…
In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To…
The efficiency of boundary element methods depends crucially on the time required for setting up the stiffness matrix. The far-field part of the matrix can be approximated by compression schemes like the fast multipole method or…
Compactness is one of the core notions of analysis: it connects local properties to global ones and makes limits well-behaved. We study the computational properties of the compactness of Cantor space $2^{\mathbb{N}}$ for uncountable covers.…
We use techniques from algebraic and extremal combinatorics to derive upper bounds on the number of independent sets in several (hyper)graphs arising from finite geometry. In this way, we obtain asymptotically sharp upper bounds for partial…
Kernel smooth is the most fundamental technique for data density and regression estimation. However, time-consuming is the biggest obstacle for the application that the direct evaluation of kernel smooth for $N$ samples needs ${O}\left(…
This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…
We describe a hybrid Fourier/direct space convolution algorithm for compact radial (azimuthally symmetric) kernels on the sphere. For high resolution maps covering a large fraction of the sky, our implementation takes advantage of the…
We introduce the notion of the (instanton part of the) Seiberg-Witten prepotential for general Schrodinger operators with periodic potential. In the case when the operator in question is integrable we show how to compute the prepotential in…
We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…
We investigate the computation of Hessian matrices via Automatic Differentiation, using a graph model and an algebraic model. The graph model reveals the inherent symmetries involved in calculating the Hessian. The algebraic model, based on…