Related papers: A rational approximation for efficient computation…
Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to address its high computational complexity, some leading to approximate or…
We study Boolean functions of an arbitrary number of input variables that can be realized by simple iterative constructions based on constant-size primitives. This restricted type of construction needs little global coordination or control…
Parameter estimation and uncertainty quantification are crucial in computational cardiology, as they enable the construction of digital twins that faithfully replicate the behavior of physical patients. Robust and efficient mathematical…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…
The calculation and manipulation of large multi-variable rational functions is a key bottleneck in multi-loop calculations. In these conference proceedings, based on my article [Chawdhry (2023) arXiv:2312.03672], I present a technique to…
We propose a new approach to discretize the von Neumann equation, which is efficient in the semi-classical limit. This method is first based on the so called Weyl's variables to address the stiffness associated with the equation. Then, by…
We consider the decision problem for quantifier-free formulas whose atoms are linear inequalities interpreted over the reals or rationals. This problem may be decided using satisfiability modulo theory (SMT), using a mixture of a SAT solver…
Spectral polynomial approximation of smooth functions allows real-time manipulation of and computation with them, as in the Chebfun system. Extension of the technique to two-dimensional and three-dimensional functions on hyperrectangles has…
A practical method to compute the Riemann zeta function is presented. The method can compute $\zeta(1/2+it)$ at any $\lfloor T^{1/4} \rfloor$ points in $[T,T+T^{1/4}]$ using an average time of $T^{1/4+o(1)}$ per point. This is the same…
This paper presents an algorithm for the efficient approximation of the saddle-extremum persistence diagram of a scalar field. Vidal et al. introduced recently a fast algorithm for such an approximation (by interrupting a progressive…
Bayesian predictive probabilities are commonly used for interim monitoring of clinical trials through efficacy and futility stopping rules. Despite their usefulness, calculation of predictive probabilities, particularly in pre-experiment…
In this document, as far as the authors know, an approximation to the zeros of the Riemann zeta function has been obtained for the first time using only derivatives of constant functions, which was possible only because a fractional…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
Rational function approximations find applications in many areas including macro-modeling of high-frequency circuits, model order reduction for controller design, interpolation and extrapolation of system responses, surrogate models for…
The widespread use of quantile regression methods depends crucially on the existence of fast algorithms. Despite numerous algorithmic improvements, the computation time is still non-negligible because researchers often estimate many…
We introduce a new class of fractional backward orthogonal functions designed for the spectral approximation of weakly singular adjoint Volterra integral equations. These basis functions generate an approximation space that naturally…
A rational function $f(x)$ is rationally summable if there exists a rational function $g(x)$ such that $f(x)=g(x+1)-g(x)$. Detecting whether a given rational function is summable is an important and basic computational subproblem that…
Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…
A simple and very accurate method to approximate a function with a finite number of discontinuities is presented. This method relies on hyperbolic tangent functions of rational arguments as connecting functions at the discontinuities, each…
We consider the global minimization of smooth functions based solely on function evaluations. Algorithms that achieve the optimal number of function evaluations for a given precision level typically rely on explicitly constructing an…