Related papers: An iterative method for computing $\pi$ by argumen…
Continuous-time algebraic Lyapunov equations have become an essential tool in various applications. In the case of large-scale sparse coefficient matrices and indefinite constant terms, indefinite low-rank factorizations have successfully…
$p$-adic continued fractions, as an extension of the classical concept of classical continued fractions to the realm of $p$-adic numbers, offering a novel perspective on number representation and approximation. While numerous $p$-adic…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
We derive a set of coupled four-dimensional integral equations for the $NN-\pi NN$ system using our modified version of the Taylor method of classification-of-diagrams. These equations are covariant, obey two and three-body unitarity and…
We apply a result of David and Jon Borwein to evaluate a sequence of highly-oscillatory integrals whose integrands are the products of a rapidly growing number of sinc functions. The value of each integral is given in the form $\pi(1-t)/2$,…
In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical…
We propose a generic algorithm for computing the inverses of a multiplicative function under the assumption that the set of inverses is finite. More generally, our algorithm can compute certain functions of the inverses, such as their power…
We introduce a new iteration method called Picard-S iteration. We show that the Picard-S iteration method can be used to approximate fixed point of contraction mappings. Also, we show that our new iteration method is equivalent and…
Designing experiments often requires balancing between learning about the true treatment effects and earning from allocating more samples to the superior treatment. While optimal algorithms for the Multi-Armed Bandit Problem (MABP) provide…
The constant $\pi$ has fascinated scholars throughout the centuries, inspiring numerous formulas for its evaluation, such as infinite sums and continued fractions. Despite their individual significance, many of the underlying connections…
In this paper, we propose a Riemannian steepest descent method for solving a blind deconvolution problem. We prove that the proposed algorithm with an appropriate initialization will recover the exact solution with high probability when the…
This study investigates computationally efficient algorithms for solving discrete-time infinite-horizon single-agent/multi-agent dynamic models with continuous actions. It shows that we can easily reduce the computational costs by slightly…
We present a unified constructive digit-by-digit framework for exact root extraction using only integer arithmetic. The core contribution is a complete correctness theory for the fractional square root algorithm, proving that each computed…
The usual formulation of efficient division uses Newton iteration to compute an inverse in a related domain where multiplicative inverses exist. On one hand, Newton iteration allows quotients to be calculated using an efficient…
The light damping hypothesis is usually assumed in structural dynamics since dissipative forces are in general weak with respect to inertial and elastic forces. In this paper a novel numerical method of time integration based on the…
Approximate computing has shown to provide new ways to improve performance and power consumption of error-resilient applications. While many of these applications can be found in image processing, data classification or machine learning, we…
Multiplicative inverse is a crucial operation in public key cryptography, and been widely used in cryptography. Public key cryptography has given rise to such a need, in which we need to generate a related public and private pair of…
By using an asymptotic formula known for the numbers of Euler and Bernoulli it is possible to obtain an explicit expression of the nth digit of $\pi$ in decimal or in binary, it also makes it possible to obtain the $n^{\rm th}$ digit of…
We present an efficient and elementary algorithm for computing the number of primes up to $N$ in $\tilde{O}(\sqrt N)$ time, improving upon the existing combinatorial methods that require $\tilde{O}(N ^ {2/3})$ time. Our method has a similar…
We study reinforcement learning in infinite-horizon average-reward settings with linear MDPs. Previous work addresses this problem by approximating the average-reward setting by discounted setting and employing a value iteration-based…