相关论文: TaylUR, an arbitrary-order diagonal automatic diff…
We introduce libdlr, a library implementing the recently introduced discrete Lehmann representation (DLR) of imaginary time Green's functions. The DLR basis consists of a collection of exponentials chosen by the interpolative decomposition…
In recent years, the use of variable-order differential operators has emerged as a powerful tool in the analysis of nonlinear fractional differential equations and chaotic systems. In finance, the accurate prediction of market trends and…
\textbf{FlexBox} is a flexible MATLAB toolbox for finite dimensional convex variational problems in image processing and beyond. Such problems often consist of non-differentiable parts and involve linear operators. The toolbox uses a…
Probability generating functionals (PGFLs) are efficient and powerful tools for tracking independent objects in clutter. It was shown that PGFLs could be used for the elegant derivation of practical multi-object tracking algorithms, e.g.,…
Numerical solutions of partial differential equations enable a broad range of scientific research. The Dedalus Project is a flexible, open-source, parallelized computational framework for solving general partial differential equations using…
We define analogues of higher derivatives for $F_q$-linear functions over the field of formal Laurent series with coefficients in $F_q$. This results in a formula for Taylor coefficients of a $F_q$-linear holomorphic function, a definition…
We present a method for the numerical calculation of derivatives of functions of general complex matrices. The method can be used in combination with any algorithm that evaluates or approximates the desired matrix function, in particular…
In scientific computation, it is often necessary to calculate higher-order derivatives of a function. Currently, two primary methods for higher-order automatic differentiation exist: symbolic differentiation and algorithmic automatic…
In this study, we establish that deep neural networks employing ReLU and ReLU$^2$ activation functions can effectively represent Lagrange finite element functions of any order on various simplicial meshes in arbitrary dimensions. We…
In this paper, a new calculus on sequences is defined. Also, the $\lambda$-derivative and the $\lambda$-integration are investigated. The fundamental theorem of $\lambda$-calculus is included. A suitable function basis for the…
The Gelfand-Yaglom formula relates functional determinants of the one-dimensional second order differential operators to the solutions of the corresponding initial value problem. In this work we generalise the Gelfand-Yaglom method by…
We derive algorithms for higher order derivative computation of the rectangular $QR$ and eigenvalue decomposition of symmetric matrices with distinct eigenvalues in the forward and reverse mode of algorithmic differentiation (AD) using…
We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is…
A numerical algorithm (implemented in Matlab) for computing the zeros of the parabolic cylinder function $U(a,z)$ in domains of the complex plane is presented. The algorithm uses accurate approximations to the first zero plus a highly…
The paper deals with a fractional derivative introduced by means of the Fourier transform. The explicit form of the kernel of general derivative operator acting on the functions analytic on a curve in complex plane is deduced and the…
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…
A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…
Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…
Transformers have been shown to be able to perform deductive reasoning on a logical rulebase containing rules and statements written in natural language. Recent works show that such models can also produce the reasoning steps (i.e., the…
Fast Fourier transform was included in the Top 10 Algorithms of 20th Century by Computing in Science & Engineering. In this paper, we provide a new simple derivation of both the discrete Fourier transform and fast Fourier transform by means…