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 ...

Computer scientists have devised an innovative and elegantly concise algorithm that can efficiently solve systems of linear equations that are critical to such important computer applications as image ...

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 ...

In 1965 Broyden introduced a family of algorithms called (rank-one) quasi-Newton methods for iteratively solving systems of nonlinear equations. We show that when any member of this family is applied ...

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 ...

It’s the sort of easy maths problem that you can work out in a few minutes using pencil and paper, but physicists in China, Canada and Singapore have now solved pairs of linear equations like this one ...

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 ...