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 ...

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 ...

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 fully derivative-free spectral residual method for solving large-scale nonlinear systems of equations is presented. It uses in a systematic way the residual vector as a search direction, a spectral ...

Simultaneous equations Simultaneous examples with no common coefficients Creating and solving simultaneous equations Simultaneous equations with linear and quadratic Solving simultaneous equations ...

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 ...

Looking for the answers to ax² + bx + c = 0? A mathematician has rediscovered a technique that the ancient Babylonians used. By Kenneth Chang and Jonathan Corum The quadratic equation has frustrated ...

Look at the National 4 factorising section before continuing. When a question asks you to 'solve' a quadratic equation, this means that you are to find the roots of the quadratic. In other words, ...