Related papers: Time- and space-efficient evaluation of the comple…
The key to the proof of the Ohsawa-Takegoshi Extension Theorem is a certain $\bar{\partial}$-estimate. The purpose of this note is to show that the 'curvature term' that arises in the Kohn-Morrey-H\"{o}rmander inequality (or the…
We compare exponential-type integrators for the numerical time-propagation of the equations of motion arising in the multi-configuration time-dependent Hartree-Fock method for the approximation of the high-dimensional multi-particle…
Numerical data processing is a key task across different fields of computer technology use. However, even simple summation of values is not precise due to the floating point representation use. This paper presents a practical algorithm for…
Time series analysis is used to understand and predict dynamic processes, including evolving demands in business, weather, markets, and biological rhythms. Exponential smoothing is used in all these domains to obtain simple interpretable…
As was initially shown by Brent, exponentials of truncated power series can be computed using a constant number of polynomial multiplications. This note gives a relatively simple algorithm with a low constant factor.
We present a novel algorithm which can overcome the drawbacks of the conventional linear scaling method with minimal computational overhead. This is achieved by introducing additional constraints, thus eliminating the redundancy of the…
In this paper, we present exact exponential algorithms for computing branchwidth that are fast both in theory and in practice. The running times of these algorithms are single-exponential in the number of vertices. Our basic algorithm is…
Let $R^{\frac{1}{2}}$ be a large integer, and $\omega$ be a nonnegative weight in the $R$-ball $B_R=[0,R]^2$ such that $\omega(B_R)\le R$. For any complex sequence $\{a_n\}$, define the quadratic exponential sum \[…
In this manuscript, we propose matrix- and tensor-oriented methods for the numerical solution of the multidimensional evolutionary space-fractional complex Ginzburg--Landau equation. After a suitable spatial semidiscretization, the…
A method for the evaluation of the epsilon expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums.…
We present a method for high-precision numerical evaluations of Lauricella functions, whose indices are linearly dependent on some parameter $\varepsilon$, in terms of their Laurent series expansions at zero. This method is based on finding…
The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…
Previous work has demonstrated that efficient algorithms exist for computing Kan extensions and that some Kan extensions have interesting similarities to various machine learning algorithms. This paper closes the gap by proving that all…
An efficient real space method is derived for the evaluation of the Madelung's potential of ionic crystals. The proposed method is an extension of the Evjen's method. It takes advantage of a general analysis for the potential convergence in…
Data-driven algorithm design is a promising, learning-based approach for beyond worst-case analysis of algorithms with tunable parameters. An important open problem is the design of computationally efficient data-driven algorithms for…
Euler's elastica model has been extensively studied and applied to image processing tasks. However, due to the high nonlinearity and nonconvexity of the involved curvature term, conventional algorithms suffer from slow convergence and high…
Exponential divided differences arise in numerical linear algebra, matrix-function evaluation, and quantum Monte Carlo simulations, where they serve as kernel weights for time evolution and observable estimation. Efficient and numerically…
The performance of numerical micromagnetic models is limited by the demagnetizing field computation, which typically accounts for the majority of the computation time. For magnetization dynamics simulations explicit evaluation methods are…
We present a fast algorithm for modular exponentiation when the factorization of the modulus is known. Let $a,n,m$ be positive integers and suppose $m$ factors canonically as $\prod_{i=1}^k p_i^{e_i}$. Choose integer parameters $t_i\in [1,…
We give an algorithm for reversion of formal power series, based on an efficient way to implement the Lagrange inversion formula. Our algorithm requires $O(n^{1/2}(M(n) + MM(n^{1/2})))$ operations where $M(n)$ and $MM(n)$ are the costs of…