Related papers: An analysis of a butterfly algorithm

We generalize the recent invariant polytope algorithm for computing the joint spectral radius and extend it to a wider class of matrix sets. This, in particular, makes the algorithm applicable to sets of matrices that have finitely many…

In this paper, we show that extending the butterfly operations from the FFT algorithm to a general Butterfly Transform (BFT) can be beneficial in building an efficient block structure for CNN designs. Pointwise convolutions, which we refer…

Approximation theorem is one of the most important aspects of numerical analysis that has evolved over the years with many different approaches. Some of the most popular approximation methods include the Lebesgue approximation theorem, the…

In this letter, we present a fast and well-conditioned spectral method based on the Chebyshev polynomials for computing the continuous part of the nonlinear Fourier spectrum. The algorithm achieves a complexity of $O(N_{\text{iter.}}N\log…

An algorithm for constructing a control function that transfers a wide class of stationary nonlinear systems of ordinary differential equations from an initial state to a final state under certain control restrictions is proposed. The…

The dragonfly algorithm was developed in 2016. It is one of the algorithms used by researchers to optimize an extensive series of uses and applications in various areas. At times, it offers superior performance compared to the most…

Structured CNN designed using the prior information of problems potentially improves efficiency over conventional CNNs in various tasks in solving PDEs and inverse problems in signal processing. This paper introduces BNet2, a simplified…

We present sparse interpolation algorithms for recovering a polynomial with $\le B$ terms from $N$ evaluations at distinct values for the variable when $\le E$ of the evaluations can be erroneous. Our algorithms perform exact arithmetic in…

Bipartite graphs characterize relationships between two different sets of entities, like actor-movie, user-item, and author-paper. The butterfly, a 4-vertices 4-edges (2,2)-biclique, is the simplest cohesive motif in a bipartite graph and…

In this paper we present a new multilevel quasi-interpolation algorithm for smooth periodic functions using scaled Gaussians as basis functions. Recent research in this area has focussed upon implementations using basis function with finite…

Bipartite graphs offer a powerful framework for modeling complex relationships between two distinct types of vertices, incorporating probabilistic, temporal, and rating-based information. While the research community has extensively…

Neville's algorithm is known to provide an efficient and numerically stable solution for polynomial interpolations. In this paper, an extension of this algorithm is presented which includes the derivatives of the interpolating polynomial.

A novel method which is called the Chebyshev inertial iteration for accelerating the convergence speed of fixed-point iterations is presented. The Chebyshev inertial iteration can be regarded as a valiant of the successive over relaxation…

Overparameterized neural networks generalize well but are expensive to train. Ideally, one would like to reduce their computational cost while retaining their generalization benefits. Sparse model training is a simple and promising approach…

Block Gram-Schmidt algorithms serve as essential kernels in many scientific computing applications, but for many commonly used variants, a rigorous treatment of their stability properties remains open. This work provides a comprehensive…

We consider the problem of counting motifs in bipartite affiliation networks, such as author-paper, user-product, and actor-movie relations. We focus on counting the number of occurrences of a "butterfly", a complete $2 \times 2$ biclique,…

We describe new developments in the OpenLoops framework based on the recently introduced on-the-fly method. The on-the-fly approach exploits the factorisation of one-loop diagrams into segments in order to perform various operations, such…

Nature-inspired metaheuristic algorithms, especially those based on swarm intelligence, have attracted much attention in the last ten years. Firefly algorithm appeared in about five years ago, its literature has expanded dramatically with…

Bipartite networks are of great importance in many real-world applications. In bipartite networks, butterfly (i.e., a complete 2 x 2 biclique) is the smallest non-trivial cohesive structure and plays a key role. In this paper, we study the…

We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…