Some algorithms based upon a projection process onto the Krylov subspace $K_m = \operatorname{Span}(r_0, Ar_0, \ldots, A^{m - 1}r_0)$ are developed, generalizing the ...

Most linear algebra courses start by considering how to solve a system of linear equations. \[ \begin{align} a_{0,0}x_0 + a_{0,1}x_0 + \cdots a_{0,n-1}x_0 & = b_0 ...

A research team at Duke University has developed a new AI framework that can uncover simple, understandable rules that govern some of the most complex dynamics found in nature and technology. The AI ...

Most linear algebra courses start by considering how to solve a system of linear equations. \[ \begin{align} a_{0,0}x_0 + a_{0,1}x_0 + \cdots a_{0,n-1}x_0 & = b_0 ...

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 ...

Solving an equation means finding the value or values for which the two expressions on each side of the equals sign are equal. One of the most common methods used to solve equations is the balance ...