Related papers: Applications of AAA rational approximation
Artificial intelligence (AI)-based models used to improve different fields including healthcare, and finance. One of the field that receive advantages of AI is automation. However, it is important to consider human factors in application of…
In the field of numerical approximation, specialists considering highly complex problems have recently proposed various ways to simplify their underlying problems. In this field, depending on the problem they were tackling and the community…
Model-free deep reinforcement learning (RL) algorithms have been widely used for a range of complex control tasks. However, slow convergence and sample inefficiency remain challenging problems in RL, especially when handling continuous and…
This work is devoted to functional ARMA$(p, q)$ processes and approximating vector models based on functional PCA in the context of prediction. After deriving sufficient conditions for the existence of a stationary solution to both the…
The goal of this paper is to explore the basic Approximate Bayesian Computation (ABC) algorithm via the lens of information theory. ABC is a widely used algorithm in cases where the likelihood of the data is hard to work with or…
The Deferred Acceptance Algorithm (DAA) is the most widely accepted and used algorithm to match students, workers, or residents to colleges, firms or hospitals respectively. In this paper, we consider for the first time, the complexity of…
We present the parallel and interacting stochastic approximation annealing (PISAA) algorithm, a stochastic simulation procedure for global optimisation, that extends and improves the stochastic approximation annealing (SAA) by using…
In this work, we show a methodology aimed to improve the quality of the assessment process for subjects related to basic programming. The method takes into account the relevance of the items and the students answers to follow different…
Advances in numerical optimization have supported breakthroughs in several areas of signal processing. This paper focuses on the recent enhanced variants of the proximal gradient numerical optimization algorithm, which combine quasi-Newton…
This note describes continued fraction representations for the rational approximations to the zeta function recently found by the author. It is tempting to think that these continued fractions might be analysed using a souped up version of…
Numerical interpolation techniques are widely employed for calculating large rational functions in scattering amplitude computations. It has been observed in recent years that these rational functions greatly simplify upon partial…
Many modern solvers and program analyzers rely on non-monotone reasoning (e.g. negation-as-failure, speculative updates, backtracking) for which classical monotone fixed-point methods do not apply. The general problem of finding the fixed…
AI agents -- systems that combine foundation models with reasoning, planning, memory, and tool use -- are rapidly becoming a practical interface between natural-language intent and real-world computation. This survey synthesizes the…
A new recalibration post-processing method is presented to improve the quality of the posterior approximation when using Approximate Bayesian Computation (ABC) algorithms. Recalibration may be used in conjunction with existing…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
We discuss the role of random basis function approximators in modeling and control. We analyze the published work on random basis function approximators and demonstrate that their favorable error rate of convergence O(1/n) is guaranteed…
Non-normal modal logics, interpreted on neighbourhood models which generalise the usual relational semantics, have found application in several areas, such as epistemic, deontic, and coalitional reasoning. We present here preliminary…
Computing the discrete rational minimax approximation in the complex plane is challenging. Apart from Ruttan's sufficient condition, there are few other sufficient conditions for global optimality. The state-of-the-art rational…
We consider the problem of approaching real numbers with rational numbers with prime denominator and with a single numerator allowed for each denominator. We obtain basic results, both probabilistic and deterministic, draw connections to…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…