Abstract: This paper investigates the average running times and complexities of various root-finding algorithms, including the Affine Method (ARM), Sparse Root Algorithm (SRA), and Branching Tree ...

Chris is a writer and editor with over 10 years of experience covering games and has a bachelor's degree in History from the University of Central Lancashire. He's mainly focused on guides, but has ...

When Edsger W. Dijkstra published his algorithm in 1959, computer networks were barely a thing. The algorithm in question found the shortest path between any two nodes on a graph, with a variant ...

The original version of this story appeared in Quanta Magazine. If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle ...

Whether you’re solving geometry problems, handling scientific computations, or processing data arrays, calculating square roots in Python is a fundamental task. Python offers multiple approaches for ...

ABSTRACT: A hybrid cryptographic system providing digital authentication is described and analyzed in this paper. The proposed cryptosystem incorporates three features: complexity of the discrete ...

Noblemen, enslaved people, freedom fighters, slaveholders: what the complex family tree of the first American pontiff reveals. Noblemen, enslaved people, freedom fighters, slaveholders: what the ...

Streaming services are helping revive America’s most old-fashioned, undigital genre. Charley Crockett, a rising star in the roots-music field, performing in Nashville, Ind., in May.Credit...Kristine ...

The digital transformation of the music industry leaves a landscape both exhilarating and unsettling. Streaming algorithms dictate playlists, AI-generated melodies flood the market, and the very ...

The original version of this story appeared in Quanta Magazine. If you’ve been making the same commute for a long time, you’ve probably settled on what seems like the best route. But “best” is a ...

The behaviour of general root-finding algorithms is studied in numerical analysis. How-ever, for polynomials, root-finding study belongs generally to computer algebra, sincealgebraic properties of ...