相关论文: An analysis of a butterfly algorithm

Accurate calculations of the spectral density in a strongly correlated quantum many-body system are of fundamental importance to study its dynamics in the linear response regime. Typical examples are the calculation of inclusive and…

Chebfun and related software projects for numerical computing with functions are based on the idea that at each step of a computation, a function $f(x)$ defined on an interval $[a,b]$ is "rounded" to a prescribed precision by constructing a…

We introduce a new method to price American options based on Chebyshev interpolation. In each step of a dynamic programming time-stepping we approximate the value function with Chebyshev polynomials. The key advantage of this approach is…

We study the bias-variance tradeoff within a multiscale approximation framework. Our approach uses a given quasi-interpolation operator, which is repeatedly applied within an error-correction scheme over a hierarchical data structure. We…

The discrete cosine transform is a valuable tool in analysis of data on undirected rectangular grids, like images. In this paper it is shown how one can define an analogue of the discrete cosine transform on triangles. This is done by…

A fast and reliable algorithm for the optimal interpolation of scattered data on the torus by multivariate trigonometric polynomials is presented. The algorithm is based on a variant of the conjugate gradient method in combination with the…

We present a one-step algorithm that solves the Maxwell equations for systems with spatially varying permittivity and permeability by the Chebyshev method. We demonstrate that this algorithm may be orders of magnitude more efficient than…

For radial basis function (RBF) kernel interpolation of scattered data, Schaback in 1995 proved that the attainable approximation error and the condition number of the underlying interpolation matrix cannot be made small simultaneously. He…

This study proposes an algorithm titled a statistical firefly algorithm (SFA) for truss topology optimization. In the proposed algorithm, historical results of fireflies' motions are used in hypothesis testing to limit the motions of…

Perturbation theory is a powerful tool for studying large-scale structure formation in the universe and calculating observables such as the power spectrum or bispectrum. However, beyond linear order, typically this is done by assuming a…

Randomized block Krylov subspace methods form a powerful class of algorithms for computing the extreme eigenvalues of a symmetric matrix or the extreme singular values of a general matrix. The purpose of this paper is to develop new…

Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics,…

Balanced butterfly counting, corresponding to counting balanced (2, 2)-bicliques, is a fundamental primitive in the analysis of signed bipartite graphs and provides a basis for studying higher-order structural properties such as clustering…

The constrained mock-Chebyshev least squares operator is a linear approximation operator based on an equispaced grid of points. Like other polynomial or rational approximation methods, it was recently introduced in order to defeat the Runge…

In this work we study and analyze a class of Duhem hysteresis operators that can exhibit butterfly loops. We study firstly the consistency property of such operator which corresponds to the existence of an attractive periodic solution when…

An explicit stabilized additive Runge-Kutta scheme is proposed. The method is based on a splitting of the problem in severely stiff and mildly stiff subproblems, which are then independently solved using a Runge-Kutta-Chebyshev scheme. The…

We analyse and compare the complexity of several algorithms for computing modular polynomials. We show that an algorithm relying on floating point evaluation of modular functions and on interpolation, which has received little attention in…

Butterflies, or 4-cycles in bipartite graphs, are crucial for identifying cohesive structures and dense subgraphs. While agent-based data mining is gaining prominence, its application to bipartite networks remains relatively unexplored. We…

Unions of graph Fourier multipliers 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 to the high-dimensional signals…

Kernel based regularized interpolation is a well known technique to approximate a continuous multivariate function using a set of scattered data points and the corresponding function evaluations, or data values. This method has some…