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We present a second order accurate in time numerical scheme for curve shortening flow in the plane that is unconditionally monotone. It is a variant of threshold dynamics, a class of algorithms in the spirit of the level set method that…

Numerical Analysis · Mathematics 2022-12-12 Selim Esedoglu , Jiajia Guo

We present a simple method to obtain the solution of a few orbital problems: the Kepler problem, the modified Kepler problem by the addition of an inverse square potential and linear force.

Classical Physics · Physics 2021-12-17 M. Moriconi

In this paper, we investigate the ``shuffle-type'' formula for special values of desingularized multiple zeta functions at integer points. It is proved by giving an iterated integral/differential expression for the desingularized multiple…

Number Theory · Mathematics 2023-02-23 Nao Komiyama , Takeshi Shinohara

We described a simple algorithm running in linear time for each fixed constant $k$, that either establishes that the pathwidth of a graph $G$ is greater than $k$, or finds a path-decomposition of $G$ of width at most $O(2^{k})$. This…

Combinatorics · Mathematics 2009-09-25 Kevin Cattell , Michael J. Dinneen , Michael R. Fellows

We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…

We present a simple algorithm for computing the document array given a string collection and its suffix array as input. Our algorithm runs in linear time using constant additional space for strings from constant alphabets.

Data Structures and Algorithms · Computer Science 2020-09-10 Felipe A. Louza

In this paper modified variants of the sparse Fourier transform algorithms from [14] are presented which improve on the approximation error bounds of the original algorithms. In addition, simple methods for extending the improved sparse…

Numerical Analysis · Mathematics 2010-10-04 M. A. Iwen

In a carsharing system, a fleet of cars is distributed at stations in an urban area, customers can take and return cars at any time and station. For operating such a system in a satisfactory way, the stations have to keep a good ratio…

Data Structures and Algorithms · Computer Science 2015-11-10 Sahar Bsaybes , Alain Quilliot , Annegret K. Wagler , Jan-Thierry Wegener

We propose a novel time stepping method for linear poroelasticity by extending a recent iterative decoupling approach to the second-order case. This results in a two-step scheme with an inner iteration and a relaxation step. We prove…

Numerical Analysis · Mathematics 2025-08-20 R. Altmann , M. Deiml

We present two types of meta-algorithm that can greatly improve the accuracy of existing algorithms for integrating the equations of motion of dynamical systems. The first meta-algorithm takes an integrator that is time-symmetric only for…

Astrophysics · Physics 2007-05-23 Piet Hut , Yoko Funato , Eiichiro Kokubo , Junichiro Makino , Steve McMillan

In this note, we present an algorithm that yields many new methods for constructing doubly stochastic and symmetric doubly stochastic matrices for the inverse eigenvalue problem. In addition, we introduce new open problems in this area that…

Spectral Theory · Mathematics 2012-02-15 Bassam Mourad , Hassan Abbas , Ayman Mourad , Ahmad Ghaddar , Issam Kaddoura

Consider a two-player zero-sum stochastic game where the transition function can be embedded in a given feature space. We propose a two-player Q-learning algorithm for approximating the Nash equilibrium strategy via sampling. The algorithm…

Machine Learning · Computer Science 2019-06-04 Zeyu Jia , Lin F. Yang , Mengdi Wang

We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…

Numerical Analysis · Mathematics 2021-11-18 João R. Cardoso , Amir Sadeghi

A constant-workspace algorithm has read-only access to an input array and may use only O(1) additional words of $O(\log n)$ bits, where $n$ is the size of the input. We assume that a simple $n$-gon is given by the ordered sequence of its…

Computational Geometry · Computer Science 2013-06-14 Tetsuo Asano , Kevin Buchin , Maike Buchin , Matias Korman , Wolfgang Mulzer , Günter Rote , André Schulz

We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…

Numerical Analysis · Mathematics 2008-02-13 Lexing Ying , Sergey Fomel

This paper proposes a new class of simple, distributed algorithms for scheduling in wireless networks. The algorithms generate new schedules in a distributed manner via simple local changes to existing schedules. The class is parameterized…

Networking and Internet Architecture · Computer Science 2007-05-23 Sujay Sanghavi , Loc Bui , R. Srikant

Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal inherent…

Signal Processing · Electrical Eng. & Systems 2020-12-16 Bin Li , Zhikang Jiang , Jie Chen

Saddle fixed points are the centerpieces of complicated dynamics in a system. The one-dimensional stable and unstable manifolds of these saddle-points are crucial to understanding the dynamics of such systems. While the problem of sketching…

Chaotic Dynamics · Physics 2022-07-13 Vaibhav Ganatra , Soumitro Banerjee

We describe an algorithm for the application of the forward and inverse spherical harmonic transforms. It is based on a new method for rapidly computing the forward and inverse associated Legendre transforms by hierarchically applying the…

Numerical Analysis · Mathematics 2021-08-31 James Bremer , Ze Chen , Haizhao Yang

Ride-pooling services, such as UberPool and Lyft Shared Saver, enable a single vehicle to serve multiple customers within one shared trip. Efficient path-planning algorithms are crucial for improving the performance of such systems. For…

Systems and Control · Electrical Eng. & Systems 2025-06-06 Pengbo Zhu , Giancarlo Ferrari-Trecate , Nikolas Geroliminis