Related papers: Time- and space-efficient evaluation of the comple…
In this paper we propose a method for proving some exponential inequalities based on power series expansion and analysis of derivations of the corresponding functions. Our approach provides a simple proof and generates a new class of…
This paper describes an $\sim {\cal O}(n)$ pre-compute technique to speed up the Karatsuba algorithm for multiplying two numbers.
This work introduces a novel, simple, and flexible method to quantify irreversibility in generic high-dimensional time series based on the well-known mapping to a binary classification problem. Our approach utilizes gradient boosting for…
Linear programming is a powerful method in combinatorial optimization with many applications in theory and practice. For solving a linear program quickly it is desirable to have a formulation of small size for the given problem. A useful…
We present efficient approximation of the error function obtained by Fourier expansion of the exponential function $\exp [{- {(t - 2 \sigma)^2}/4}]$. The error analysis reveals that it is highly accurate and can generate numbers that match…
Change-point problems have appeared in a great many applications for example cancer genetics, econometrics and climate change. Modern multiscale type segmentation methods are considered to be a statistically efficient approach for multiple…
Leveraging matrix sparsity has proven a fruitful strategy for accelerating quantum chemical calculations. Here we present the hierarchical SOS-MP2 algorithm, which uses hierarchical matrix ($\mathcal{H}^{2}$) compression of the electron…
Here, we give an algorithm for deciding if the nonnegative rank of a matrix $M$ of dimension $m \times n$ is at most $r$ which runs in time $(nm)^{O(r^2)}$. This is the first exact algorithm that runs in time singly-exponential in $r$. This…
We present a technique, based on so-called word series, to write down in a systematic way expansions of the strong and weak local errors of splitting algorithms for the integration of Stratonovich stochastic differential equations. Those…
We demonstrate that a modification of the classical index calculus algorithm can be used to factor integers. More generally, we reduce the factoring problem to finding an overdetermined system of multiplicative relations in any factor base…
While the Karatsuba algorithm reduces the complexity of large integer multiplication, the extra additions required minimize its benefits for smaller integers of more commonly-used bitwidths. In this work, we propose the extension of the…
The exponentially convergent trapezoidal rule is applied to a suitable integral representation of the Faddeeva function to derive a simple formula for its evaluation. I describe its properties, strategies for maximising its efficiency, and…
We present fast classification techniques for sparse generalized linear and additive models. These techniques can handle thousands of features and thousands of observations in minutes, even in the presence of many highly correlated…
In this paper, we consider the task of efficiently computing the numerical solution of evolutionary complex Ginzburg--Landau equations on Cartesian product domains with homogeneous Dirichlet/Neumann or periodic boundary conditions. To this…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
The quality of numerical computations can be measured through their forward error, for which finding good error bounds is challenging in general. For several algorithms and using stochastic rounding (SR), probabilistic analysis has been…
We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual…
We design algorithms for computing values of many p-adic elementary and special functions, including logarithms, exponentials, polylogarithms, and hypergeometric functions. All our algorithms feature a quasi-linear complexity with respect…
Binary segmentation is the classic greedy algorithm which recursively splits a sequential data set by optimizing some loss or likelihood function. Binary segmentation is widely used for changepoint detection in data sets measured over space…
This paper deals with the evaluation of double line integrals of the squared exponential covariance function. We propose a new approach in which the double integral is reduced to a single integral using the error function. This single…