This is a preview. Log in through your library . Abstract It is well known that a damped or underrelaxed Newton's method will sometimes solve a system of nonlinear equations when the full Newton's ...

In general, when a quasi-Newton method is applied to solve a system of nonlinear equations, the quasi-Newton direction is not necessarily a descent direction for the norm function. In this paper, we ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...

Polynomial equations are a cornerstone of modern science, providing a mathematical basis for celestial mechanics, computer graphics, market growth predictions and much more. But although most high ...

AlphaProof and AlphaGeometry 2 are steps toward building systems that can reason, which could unlock exciting new capabilities. AI models can easily generate essays and other types of text. However, ...

These attempts would never solve my problem outright, but they might garner evidence toward an answer. My lack of programming expertise and resulting impatience slowed the process, making it an ...

Grade school math students are likely familiar with teachers admonishing them not to just guess the answer to a problem. But a new proof establishes that, in fact, the right kind of guessing is ...

To mathematicians, equations are art. Just as many are moved by a painting or piece of music, to those who appreciate and understand math, expressions of numbers, variables, operations and relations ...

This is a classic introductory physics problem. Basically, you have a cart on a frictionless track (call this m 1) with a string that runs over a pulley to another mass hanging below (call this m 2).