Related papers: A simple algorithm for the evaluation of the hyper…
Simulating a cellular automaton (CA) for t time-steps into the future requires t^2 serial computation steps or t parallel ones. However, certain CAs based on an Abelian group, such as addition mod 2, are termed ``linear'' because they obey…
In this work, we introduce metrics to evaluate the use of simplified time series in the context of interpretability of a TSC -- a Time Series Classifier. Such simplifications are important because time series data, in contrast to text and…
As modeling and visualization applications proliferate, there arises a need to simplify large polygonal models at interactive rates. Unfortunately existing polygon mesh simplification algorithms are not well suited for this task because…
We present a parallel approximation algorithm for a class of mixed packing and covering semidefinite programs which generalize on the class of positive semidefinite programs as considered by Jain and Yao [2011]. As a corollary we get a…
Analytic smooth solutions of a general, strongly parabolic semi-linear Cauchy problem of $2m$-th order in $\mathbb{R}^N\times (0,T)$ with analytic coefficients (in space and time variables) and analytic initial data (in space variables) are…
This manuscript proposes a probabilistic framework for algorithms that iteratively solve unconstrained linear problems $Bx = b$ with positive definite $B$ for $x$. The goal is to replace the point estimates returned by existing methods with…
We present a modification of Simon's algorithm that in some cases is able to fit experimentally obtained data to appropriately chosen trial functions with high probability. Modulo constants pertaining to the reliability and probability of…
Local polynomial regression (Fan and Gijbels 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time…
A fast algorithm is presented for determining the linear complexity and the minimal polynomial of periodic sequences over GF(q) with period q n p m, where p is a prime, q is a prime and a primitive root modulo p2. The algorithm presented…
The Classic Howard's algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial characteristic of the method is the…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
Linear complexity is an important parameter for arrays that are used in applications related to information security. In this work we survey constructions of two and three dimensional arrays, and present new results on the multidimensional…
High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…
We present two algorithms for computing hypergeometric solutions of second order linear differential operators with rational function coefficients. Our first algorithm searches for solutions of the form \[ \exp(\int r \,…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
An extremely scalable linear-algebraic algorithm was developed for quantum material simulation (electronic state calculation) with 10$^8$ atoms or 100-nm-scale materials. The mathematical foundation is generalized shifted linear equations…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided…
A new algorithm for computing coefficients of the Baker--Campbell--Hausdorff series is presented, which can be straightforwardly implemented in any general-purpose programming language or computer algebra system. The algorithm avoids…
Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By…