Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...

Abstract: This paper presents a novel hardware approach for solving systems of linear equations by leveraging in-memory computing (IMC) with memristive crossbar arrays. Unlike conventional ...

Dr. James McCaffrey from Microsoft Research presents a complete end-to-end demonstration of computing a matrix inverse using the Newton iteration algorithm. Compared to other algorithms, Newton ...

A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations. Polynomials are equations involving a variable raised to powers, such ...

Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. In this work, we describe the development of a new algorithm for the computation of ...

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...

Presenting an algorithm that solves linear systems with sparse coefficient matrices asymptotically faster than matrix multiplication for any ω > 2. Our algorithm can be viewed as an efficient, ...

On March 21, NASA announced the confirmation of the 5,000th planet outside our Solar System. From scorching-hot gas giants nestled near their parent star to rocky worlds that may host water on their ...

Dr. James McCaffrey of Microsoft Research presents a full-code, step-by-step tutorial on an implementation of the technique that emphasizes simplicity and ease-of-modification over robustness and ...